## Important Questions Class 11 Maths Chapter 11 Conic Sections

Q1. Find the equation of the parabola, if the focus is at (0, -3) and the vertex is at (0, 0).

Q2. Find the vertex, focus, axis, directrix, and latus–rectum of the following parabolas

(i) y^{2} = 8x

(ii) 4x^{2} + y = 0

Ans:

Vertex (0,0),

Focus : (0, -1/16)

Axis: Y-Axis

Directrix: y=1/16

Latus Rectum=1/4 units.

Q3. If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its center.

Q4. Find the equation of the circle which touches the x-axis and whose center is (1,2).

Q5. If one end of a diameter of the circle x^{2} + y^{2} -4x -6y + 11 = 0 is (3,4), then find the coordinate of the other end of the diameter.

Q6. Find the equation of the circle having (1, -2) as its center and passing through 3x +y= 14, 2x + 5y = 18.

Q7. Find the equation of a circle concentric with the circle x^{2} +y^{2} – 6x + 12y + 15 = 0 and has double its area.

Q8. If the latus rectum of an ellipse is equal to half of the minor axis, then find its eccentricity.

Q9. Given the ellipse with equation 9X^{2} + 25y^{2} = 225, find the eccentricity and foci.

Q10. If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10, then find the latus rectum of the ellipse.