{"id":55782,"date":"2025-01-28T12:46:07","date_gmt":"2025-01-28T07:16:07","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=55782"},"modified":"2026-02-25T04:34:41","modified_gmt":"2026-02-24T23:04:41","slug":"ex-1-draw-the-graphs-of-two-circles-and-determine-whether-they-touch-each-other-externally-or-internally","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=55782","title":{"rendered":"Ex &#8211; 1 Draw the graphs of two circles and determine whether they touch each other externally or internally"},"content":{"rendered":"\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-89bfda0d449bddcb20c4924e685a3000\">Aim:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{To draw the graph of given equation of the circles}\\ \\hspace{15cm}\\\\ x^2\\ +\\ y^2\\ -\\ 4x\\ +\\ 6y\\ +\\ 8\\ =\\ 0\\ and\\ \\hspace{10cm}\\\\ x^2\\ +\\ y^2\\ -\\ 4x\\ +\\ 6y\\ +\\ 8\\ =\\ 0\\ \\hspace{10cm}\\] <script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[a)\\ \\text{To graph the equations of the circles in the Cartesian plane.}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[b)\\ \\text{To determine the coordinates of the centres and radii of the circles and}\\ \\hspace{15cm}\\\\ \\text{mark them on the graph}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[c)\\ \\text{To determine the distance between the centres of the circles}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[d)\\ \\text{To determine whether the circles are touching eah other or not}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[e)\\ \\text{If the circles are touching each other, determine whether they are}\\ \\hspace{15cm}\\\\ \\text{touching internally or externally.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[f)\\ \\text{Verify whether any of the relationships}\\ \\hspace{20cm}\\\\ C_1C_2\\ =\\ r_1\\ +\\ r_2\\ or\\ C_1C_2\\ =\\ |r_1\\ -\\ r_2|\\ holds\\ or\\ not.\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-caaadd60b535c837691a2eb0c3ab170e\">Procedure:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To draw the graph of the given circle}\\ x^2\\ +\\ y^2\\ -\\ 4x\\ +\\ 6y\\ +\\ 8\\ =\\ 0\\ \\hspace{18cm}\\\\ \\text{by using the input bar type x^2 + y^2 &#8211; 4x + 6y + 8 = 0 and press Enter Key.}\\ \\hspace{10cm}\\\\ \\text{The graph of the given circle appears in the graphics view and}\\ \\hspace{10cm}\\\\ \\text{named as eq1 in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{Similarly, to draw the graph of the given circle}\\ x^2\\ +\\ y^2\\ -\\ 10x\\ -\\ 6y\\ +\\ 14\\ =\\ 0\\ \\hspace{18cm}\\\\ \\text{by using the input bar type x^2 + y^2 &#8211; 10x &#8211; 6y + 14\n = 0 and press Enter Key.}\\ \\hspace{10cm}\\\\ \\text{The graph of the given circle appears in the graphics view and}\\ \\hspace{10cm}\\\\ \\text{named as eq2 in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To determine the center of the circle eq1 by using the input bar type}\\ \\hspace{18cm}\\\\ C1\\ =\\ Center(eq1)\\ \\text{and press Enter Key.}\\ \\hspace{15cm}\\\\ \\text{Centre of the circle C1}\\ \\text{appears in the graphics view}\\ \\hspace{10cm}\\\\ \\text{and coordinates of the C1 appears in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{Similarly, to determine the center of the circle eq2 by using the input bar type}\\ \\hspace{18cm}\\\\ C2\\ =\\ Center(eq2)\\ \\text{and press Enter Key.}\\ \\hspace{15cm}\\\\ \\text{Centre of the circle C2 appears in the graphics view}\\ \\hspace{10cm}\\\\ \\text{and coordinates of the C 2 appears in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To measure the radius of the circle eq1 by using the input bar type}\\ \\hspace{18cm}\\\\ R1\\ =\\ radius(eq1)\\ \\text{and press Enter Key.}\\ \\hspace{15cm}\\\\ \\text{value of the radius of the circle eq 1 appears in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{Similarly, to measure the radius of the circle eq2 by using the input bar type}\\ \\hspace{18cm}\\\\ R2\\ =\\ radius(eq2)\\ \\text{and press Enter Key.}\\ \\hspace{15cm}\\\\ \\text{value of the radius of the circle eq 2 appears in the algebra view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{To draw the radius of the circle 1 and circle 2,}\\ \\hspace{16cm}\\\\ \\text{choose point tool, select point on the object tool.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{Plot the points on the two circles and}\\ \\hspace{18cm}\\\\ \\text{name it as A and B appears on the graphics view.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 10:}\\ \\text{To draw a segment point A to center C1,}\\ \\hspace{18cm}\\\\ \\text{choose, line tool, select segment tool.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 11:}\\ \\text{Select the points A and  C1 successively,}\\ \\hspace{18cm}\\\\ \\text{the segment appears in the graphics view and renamed as r1}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 12:}\\ \\text{Similarly select the points B and C2 successively,}\\ \\hspace{18cm}\\\\ \\text{the segment appears in the graphics view and renamed as r2}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 13:}\\ \\text{Similarly, select the points C1 and C2 successively,}\\ \\hspace{18cm}\\\\ \\text{the segment appears in the graphics view and renamed as d,}\\ \\hspace{15cm}\\\\ \\text{the value of the d appears in the algebra view.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 14:}\\ \\text{Verify whether}\\ d = R1\\ +\\ R2\\ or\\ d = |R1\\ -\\ R2|\\ \\hspace{19cm}\\\\ \\text{by using the input bar type}\\ R1\\ +\\ R2\\ or\\ abs(R1\\ -\\ R2)\\ \\text{and press Enter Key.}\\ \\hspace{10cm}\\\\ \\text{the values of the} R1\\ +\\ R2\\ or\\ abs(R1\\ -\\ R2)\\ \\hspace{10cm}\\\\  \\text{appears in the algebra view.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 15:}\\ \\text{To create input box for circle}\\ C1\\ and\\ with\\ eq1,\\ \\hspace{18cm}\\\\ \\text{choose the action object tool then select the input box tool}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 16:}\\ \\text{The popup window appears on the graphics view,}\\ \\hspace{18cm}\\\\ \\text{select input Box, click on the graphics view}\\ \\hspace{15cm}\\\\ \\text{the window appears. Type the caption Circle 1, then linked Object eq1.}\\ \\hspace{10cm}\\\\ \\text{Then press Enter key, input box appears on the graphics view}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 17:}\\ \\text{Similarly create an input box for Circle 2}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center\">Output for the touching Circles<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table class=\"has-fixed-layout\"><tbody><tr><td><\/td><td>Circle1<\/td><td>Circle2<\/td><\/tr><tr><td>Equation<\/td><td><mathml>\\[(x-2)^2\\ +\\ (y+3)^2\\ =\\ 5\\]<\/mathml><\/td><td><mathml>\\[(x-5)^2\\ +\\ (y-3)^2\\ =\\ 5\\]<\/mathml><\/td><\/tr><tr><td>Centre<\/td><td>C1 = (2, -3)<\/td><td>C2 = (5,3)<\/td><\/tr><tr><td>Radius<\/td><td>R1 = 2.24<\/td><td>R2 =4.47<\/td><\/tr><tr><td>C1C2: the distance between the centres<\/td><td>d = 6.71<\/td><td><\/td><\/tr><tr><td>R1 + R2<\/td><td>6.71<\/td><td><\/td><\/tr><tr><td>|R1 &#8211; R2|<\/td><td>2.24<\/td><td><\/td><\/tr><tr><td>C1C2 = R1 + R2<\/td><td>Yes <\/td><td><\/td><\/tr><tr><td>C1C2 = |R1 &#8211; R2|<\/td><td>No<\/td><td><\/td><\/tr><tr><td>Conclusion<\/td><td>Touching  Externally<\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/7TuyY1PmXSo\" title=\"Drawing of two circles and check they touch each other externally or internally using Geogebra\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n\n\n\n<p class=\"has-text-align-center\">Output for verification of touching circles graphically<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>S.No<\/td><td>Circle1<\/td><td>Circle2<\/td><td>Contact type<\/td><\/tr><tr><td>1.<\/td><td><mathml>\\[x^2\\ +\\ y^2\\ -\\ 4x\\ -\\ 6y\\ +\\ 9\\ =\\ 0\\]<\/mathml><\/td><td><mathml>\\[x^2\\ +\\ y^2\\ +\\ 2x\\ +\\ 2y\\ -\\ 7\\ =\\ 0\\]<\/mathml><\/td><td><\/td><\/tr><tr><td>2.<\/td><td><mathml>\\[x^2\\ +\\ y^2\\ +\\ 2x\\  -\\ 8\\ =\\ 0\\]<\/mathml><\/td><td><mathml>\\[x^2\\ +\\ y^2\\ -\\ 6x\\ +\\ 6y\\ -\\ 46\\ =\\ 0\\]<\/mathml><\/td><td><\/td><\/tr><tr><td>3.<\/td><td><mathml>\\[x^2\\ +\\ y^2\\ -\\ 8x\\ -\\ 2y\\ +\\ 16\\ =\\ 0\\]<\/mathml><\/td><td><mathml>\\[3x^2\\ +\\ 3y^2\\ -\\ 14x\\ +\\ 23y\\ -\\ 15\\ =\\ 0\\]<\/mathml><\/td><td><\/td><\/tr><tr><td>4.<\/td><td><mathml>\\[x^2\\ +\\ y^2\\ -\\ 8x\\ +\\ 6y\\ -\\ 23\\ =\\ 0\\]<\/mathml><\/td><td><mathml>\\[x^2\\ +\\ y^2\\ -\\ 2x\\ -\\ 5y\\ +\\ 16\\ =\\ 0\\]<\/mathml><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure: Output: Output for the touching Circles Circle1 Circle2 Equation \\[(x-2)^2\\ +\\ (y+3)^2\\ =\\ 5\\] \\[(x-5)^2\\ +\\ (y-3)^2\\ =\\ 5\\] Centre C1 = (2, -3) C2 = (5,3) Radius R1 = 2.24 R2 =4.47 C1C2: the distance between the centres d = 6.71 R1 + R2 6.71 |R1 &#8211; R2| 2.24 C1C2 = R1 [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":55816,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-55782","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ex - 1 Draw the graphs of two circles and determine whether they touch each other externally or internally - YANAMTAKSHASHILA<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/yanamtakshashila.com\/?p=55782\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ex - 1 Draw the graphs of two circles and determine whether they touch each other externally or internally - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"Aim: Procedure: Output: Output for the touching Circles Circle1 Circle2 Equation [(x-2)^2 + (y+3)^2 = 5] [(x-5)^2 + (y-3)^2 = 5] Centre C1 = (2, -3) C2 = (5,3) Radius R1 = 2.24 R2 =4.47 C1C2: the distance between the centres d = 6.71 R1 + R2 6.71 |R1 &#8211; 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