Parabola

If P is a point on the line x + 4a = 0 and QR is the chord of contact of P with respect to y² = 4ax, then ∠QOR (where O is the vertex) is equal to

 (A)  45°

(B)  60°

(C)  30°

(D)  90°

If two tangents to a parabola make complementary angles with the axis, then show that their point of intersection lies on the line x = a.

Find the vertex, focus, directrix and latus rectum of the parabola y² + 4x – 2y + 3 = 0.

Find the coordinates of the point whose chord of contact with respect to the parabola y² + 4x is 2x – 7y + 2 = 0

The foci of a hyperbola coincide with the foci of the ellipse \(\rm \frac{x^2}{25}+\frac{y^2}{16}=1\), find the equation of the hyperbola if its eccentricity is 3.

If 2x + y + k = 0 is a normal to the parabola y² = − 8x, then the value of k is

(A)  12

(B)   24

(C)  − 12

(D)  − 24

Show that the chords of contacts of points on the line 2x – 3y + 4 = 0 with respect to the parabola y² = 4ax pass through a fixed point.

Suppose the normals at three different points on the parabola y² = 4x pass through the point (h, 0). Show that h > 2