Part – A Prove that the equation x2 – 2xy + y2 – 16x – 12y + 22 = 0 is a parabola. Soln: x2 – 2xy + y2 – 16x – 12y + 22 = 0 —————– ( 1 ) Condition for ( 1 ) to represent parabola is h2 = ab From ( 1 ) a = 1, b = 1 2h = -2 ⇒ h = -1 h2 = ab (-1)2 = 1 ( 1) 1 = 1 1 = 1. ∴ ( 1 ) represents a…
Read MorePart – A Prove that the equation x2 – 2xy + y2 – 16x – 12y + 22 = 0 is a parabola. 2. Show that the equation 7×2 + 3xy + 2y2 – x + 2y – 1 = 0 represents an ellipse. Part – C Find axis, vertex, focus and equation of directrix for y2 + 4x + 6y + 17 = 0.
Read MorePart – A 1. Find the equation of the circle with centre (1, -2) and radius 5 units. Soln: We know that the equation of circle is (x – h )2 + (y – k )2 = r2 Here h = 1, k = – 2 (given) and r = 5 (x – 1 )2 + (y + 2 )2 = 52 x2 – 2x + 1+ y2 + 4y + 4= 25 x2 + y2 – 2x + 4y + 5 -25 = 0 x2 + y2 –…
Read MorePart – A 1. Find the equation of the circle with centre (1, -2) and radius 5 units. 2. Find the centre and radius of the circle x2 + y2 + 10x + 8y + 5 = 0 . 3. Find the equation of the circle passing through the point (1 , 1 ) and concentric to the circle x2 + y2 + 4x + 6y – 15 = 0. Part – B 1. Find the equation of the circle passing through the point A (2, 3) and having its centre at…
Read MorePart – A 1. Find the perpendicular distance from the point (3, -5) to the straight line 3x-4y-26=0. Soln: W.K.T The length of the perpendicular distance from (x1,y1) to the line ax + by + c = 0 is ± (ax1 + by1 + c)/ √(a2 + b2 ) Given straight line is 3x-4y-26 =0 Given point (x1,y1) = (3, -5) i.e ± 3(3) – 4(-5) – 26/ √(32 + (-4)2 ) = 3 / 5 2. Find the distance between the line 3x+4y = 9 and 6x+8y = 15. Soln: W.K.T …
Read MorePart – A 1. Find the perpendicular distance from the point (3, -5) to the straight line 3x-4y-26=0. 2. Find the distance between the line 3x+4y = 9 and 6x+ 8y = 15. 3. Show that the lines 3x+2y+9=0 and 12x+8y-15 =0 are parallel. 4. Find ‘p’ such that the lines 3x+4y = 8 and px + 2y = 7 are parallel. 5. Show that the lines 27x-18y+25 =0 and 2x + 3y+7 =0 are perpendicular. 6. Find the value of k if the lines 2x + ky -11 =0 and 5x…
Read MoreConic: A conic is defined as the locus of a point which moves such that its distance from a fixed point is always ‘e’ times its distance from a fixed straight line. Focus: The fixed point is called the focus of the conic. Directrix: The fixed straight line is called the directrix of the conic. Eccentricity: The constant ratio is called the eccentricity of the conic. General equation of a conic ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents (i) a circle if a…
Read MoreEQUATION OF CIRCLE Definition: A circle is the locus of a point which moves in a plane in such a way that its distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle. Equation of the circle with centre (h, k) and radius ‘r’ units. CP = r √(( x – h )2 + (y – k )2 = r (Using distance formula) (x – h )2 + (y – k )2…
Read MoreUNIT – I ANALYTICAL GEOMETRY 1.1 ANALYTICAL GEOMETRY I Straight Line: When a variable point moves in accordance with a geometrical law, the point will trace some curve. This curve is known as the locus of the variable point. If a relation in x and y represent a curve then (i) The co-ordinates of every point on the curve will satisfy the relation. (ii) Any point whose co-ordinates satisfy the relation will lie on the curve. Straight line is a locus of a point. https://clnk.in/qfwg Slope or gradient of a…
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