Practice Problems for Class 11 Maths Chapter 11 Conic Sections

1. 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: x² + y² + 2x -3y=0)
2. Determine the equation of the circle passing through the points – (0,0)(5,0) and (3,3). (Solution: x² + y² – 5x -y =0), centre (5/2 , ½) and radius = √ 26/2).
3. If the distance between the foci of a hyperbola is 16 and eccentricity is √ 2, then obtain its equation. (Solution: x² – y² =32)
4. 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)
5. Determine the equation of the ellipse whose foci are (4,0) and (-4,0), eccentricity = ⅓. (Solution: x² / 9 + y²/8 = 16)
6. Write the equation of the parabola whose vertex is at (-3,0) and the directrix is (x + 5 ) = 0. (Solution: y² = 8(x + 3))
7. AB is a double ordinate of a parabola y² = 4px. Find the locus of its points of trisection. (Solution: 9y² =4px)
8. 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).
9. Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0, and lx +my = 1. (Solution: x² + y² – (1/l)x – (1/m)y = 0)
10. Prove that the points (9,1) ( 7,9) (-2, 12), and (6,10) are concyclic.
11. Find the equation of an ellipse whose eccentricity is 2/3, latus rectum is 5 and the center is (0,0).
12. Find the equation of the circle which touches the x-axis and whose center is (1,2).
13. Find the coordinates of a point on the parabola y²=8x whose focal distance is 4.