## Practice Problems for Class 11 Maths Chapter 11 Conic Sections

- Calculate the equation of a circle that passes through the origin and cuts off intercepts -2 and 3 from the axis and the y-axis respectively. (Solution: x
^{2}+ y^{2}+ 2x -3y=0) - Determine the equation of the circle passing through the points – (0,0)(5,0) and (3,3). (Solution: x
^{2}+ y^{2}– 5x -y =0), centre (5/2 , ½) and radius = √ 26/2). - If the distance between the foci of a hyperbola is 16 and eccentricity is √ 2, then obtain its equation. (Solution: x
^{2}– y^{2}=32) - If a latus rectum of an ellipse subtends a right angle at the center of the ellipse, then write the eccentricity of the ellipse. (Solution: (√ 5 – 1) / 2)
- Determine the equation of the ellipse whose foci are (4,0) and (-4,0), eccentricity = ⅓. (Solution: x
^{2}/ 9 + y^{2}/8 = 16) - Write the equation of the parabola whose vertex is at (-3,0) and the directrix is (x + 5 ) = 0. (Solution: y
^{2}= 8(x + 3)) - AB is a double ordinate of a parabola y
^{2}= 4px. Find the locus of its points of trisection. (Solution: 9y^{2}=4px) - Calculate the equation of the parabola whose focus is (1, -1) and whose vertex is (2,1). Also, find its axis and latus-rectum). (Solution: 4 √ 5).
- Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0, and lx +my = 1. (Solution: x
^{2}+ y^{2}– (1/l)x – (1/m)y = 0) - Prove that the points (9,1) ( 7,9) (-2, 12), and (6,10) are concyclic.
- Find the equation of an ellipse whose eccentricity is 2/3, latus rectum is 5 and the center is (0,0).
- Find the equation of the circle which touches the x-axis and whose center is (1,2).
- Find the coordinates of a point on the parabola y
^{2}=8x whose focal distance is 4.

Practice Problems for Class 11 Maths Chapter 11 Conic Sections