{"id":54759,"date":"2025-01-05T19:27:23","date_gmt":"2025-01-05T13:57:23","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=54759"},"modified":"2026-02-26T16:27:55","modified_gmt":"2026-02-26T10:57:55","slug":"ex-1-draw-the-graphs-of-parabolas-and-determine-the-vertex-focus-axis-directrix-latus-rectum-using-geogebra-classic-5","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=54759","title":{"rendered":"Draw the graphs of Parabolas and determine the vertex, focus, axis, directrix , latus rectum using Geogebra classic 5"},"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{Do the following actives.}\\ \\hspace{15cm}\\]<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\">\\[i).\\ \\text{Draw the graphs of the parabolas}\\ (y\\ -\\ k)^2\\ = 4\\ a\\ (x\\ -\\ h)\\ and\\ (x\\ -\\ h)^2\\ = 4\\ a\\ (y\\ -\\ k)\\ \\hspace{10cm}\\]\\[\\text{for the given values of a, h and k}\\ \\hspace{5cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii).\\ \\text{Determine the vertex, focus, axis, directrix, latus rectum of each parabola and}\\ \\hspace{10cm}\\]\\[\\text{mark them on the graphs.}\\ \\hspace{2cm}\\ \\text{[Data set: a = 2, h = 5, k = 2] }\\ 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class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{Make graph centre}\\ \\hspace{17cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To bring Input bar up: right click \u2192 Click graphics \u2192 Preferences \u2192 Layout tab}\\ \\hspace{3cm}\\ \\\\ \\hspace{1cm}\\ \\text{\u2192 Input Bar \u2192 Click show up box}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{Create the sliders for a, h &amp; K: Tool bar \u2192 Slider tool \u2192 Click slider \u2192}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{click the mouse cursor in graph \u2192rectangular box open \u2192 under name: type &#8216;a&#8217; \u2192 click ok.}\\\\ \\text{ Then set a = 2, h = 5 and k = 2.}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{To draw the parabola: Input bar \u2192 parabola:}\\ (y-k)^2\\ =\\ 4a(x-h)\\ \\text{\u2192 Enter \u2192}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{right click on parabola \u2192 object properties \u2192 colour the parabola}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To find vertex: Input bar \u2192 V:vertex(conic) \u2192 V:vertex(parabola) \u2192 right click on V \u2192}\\\\ \\text{object properties \u2192 Put tick in the check box of Name and value \u2192 give colour to V}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{To find vertex: Input bar \u2192 F:focus(conic) \u2192 F:vertex(parabola) \u2192 right click on F \u2192}\\\\ \\text{object properties \u2192 Put tick in the check box of Name and value \u2192 give colour to F}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{To find the distance of focus from vertex:  Input bar \u2192 d:segment(point; point) \u2192}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{d:segment(V, F)\u2192 right click on d \u2192object properties \u2192 Put tick }\\\\ \\text{in the check box of Name and value \u2192 give colour to d}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{To find the Axis: Input bar \u2192 Axis:line(point; point) \u2192\nAxis:line(V, F)\u2192}\\\\ \\text{right click on Axis \u2192object properties \u2192 give colour to Axis}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 10:}\\ \\text{To find the Directrix: Input bar \u2192 Directrix:Directrix(conic;) \u2192\n}\\ \\hspace{5cm}\\\\ \\text{Directrix:Directrix(parabola)\u2192 right click on Directrix \u2192object properties \u2192 give colour to Directrix}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 11}\\ \\text{To find the Latus Rectum: Tool bar \u2192 Select Perpendicular tool \u2192 Click F(focus) and Axis)\n}\\\\ \\text{\u2192 right click on latus rectum \u2192object properties \u2192 give colour to latus rectum}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 12:}\\ \\text{To find the length of Latus Rectum: Tool bar \u2192 Select intersection tool \u2192 click latus rectum \n}\\ \\hspace{5cm}\\\\ \\text{and parabola\u2192 right click on point B \u2192Put tick in the check box of Name and value}\\ \\hspace{8cm}\\\\  \\hspace{1cm}\\ \\text{\u2192 give colour to B \u2192 right click on point A \u2192Put tick in the check box}\\  \\hspace{8cm}\\\\ \\hspace{1cm}\\ \\text{of Name and value \u2192give colour to A \u2192 segment(point : point) }\\ \\hspace{8cm}\\\\ \\hspace{1cm}\\ \\text{\u2192 segment(A, B)\u2192 right click on AB \u2192object properties \u2192Put tick}\\ \\hspace{8cm}\\\\ \\hspace{1cm}\\ \\text{in the check box of Name and value\u2192 give colour to AB \u2192 hide latus rectum}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 13:}\\ \\text{Write all the values from Algebraic view in the output box against first parabola}\\\\ (y-k)^2 = 4 a (x-h)\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 14:}\\ \\text{To determine all the values for the second parabola}\\ (x-h)^2\\ =\\ 4a(y-k): \\ \\hspace{10cm}\\\\  \\hspace{1cm}\\ \\text{Tool bar\u2192 select Input box  under slider tool \u2192 Click the mouse cursor in the graph \u2192}\\ \\hspace{10cm}\\\\ \\hspace{1cm}\\ \\text{pop up rectangular box opens up \u2192 Type &#8220;Equation=&#8221; under caption \u2192 assigned to parabola}\\ \\hspace{10cm}\\\\ \\hspace{1cm}\\  (y-k)^2 = 4*a*(x-h)\\ \\text{ \u2192 Enter \u2192 one box pops up \u2192 replace the first parabola with}\\ \\hspace{10cm}\\\\ \\hspace{1cm}\\ \\text{ second parabola \u2192 That&#8217;s it \u2192 parabola diagram will change \u2192}\\ \\hspace{10cm}\\\\ \\hspace{1cm}\\ \\text{as well as its algebraic values \u2192 Write all the values from Algebraic view in }\\ \\hspace{10cm}\\\\ \\text{the output box against first parabola}\\ (y-k)^2 = 4 a (x-h)\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<p style=\"margin-top:0;margin-right:0;margin-bottom:0;margin-left:0\"><\/p>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/_eCbVjeeCRw\" title=\"Draw the graphs of the Parabolas (y-k)^2=4a(x-h) and (x-h)^2=4a(y-k) - GeoGebra classic 5 - Modified\" 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<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 parabolas<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Equation of the Parabola<\/td><td class=\"has-text-align-center\" data-align=\"center\"><mathml>\\[(y-k)^2\\ =\\ 4\\ a\\ (x\\ -\\ h)\\]<\/mathml><\/td><td class=\"has-text-align-center\" data-align=\"center\"><mathml>\\[(x-h)^2\\ =\\ 4\\ a\\ (y\\ -\\ h)\\]<\/mathml><\/td><\/tr><tr><td>Vertex<\/td><td class=\"has-text-align-center\" data-align=\"center\">(5,2)<\/td><td class=\"has-text-align-center\" data-align=\"center\">(5,2)<\/td><\/tr><tr><td>Focus<\/td><td class=\"has-text-align-center\" data-align=\"center\">(7,2)<\/td><td class=\"has-text-align-center\" data-align=\"center\">(5,4)<\/td><\/tr><tr><td>Distance from vertex to focus<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td>Axis<\/td><td class=\"has-text-align-center\" data-align=\"center\">y = 2<\/td><td class=\"has-text-align-center\" data-align=\"center\">x = 5<\/td><\/tr><tr><td>Directrix<\/td><td class=\"has-text-align-center\" data-align=\"center\">x = 3<\/td><td class=\"has-text-align-center\" data-align=\"center\">y = 0<\/td><\/tr><tr><td>Latus rectum<\/td><td class=\"has-text-align-center\" data-align=\"center\">x = 7<\/td><td class=\"has-text-align-center\" data-align=\"center\">y = 4<\/td><\/tr><tr><td>Length of latus rectum<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure Output: Output for parabolas Equation of the Parabola \\[(y-k)^2\\ =\\ 4\\ a\\ (x\\ -\\ h)\\] \\[(x-h)^2\\ =\\ 4\\ a\\ (y\\ -\\ h)\\] Vertex (5,2) (5,2) Focus (7,2) (5,4) Distance from vertex to focus 2 2 Axis y = 2 x = 5 Directrix x = 3 y = 0 Latus rectum x = [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":55504,"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 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