Find the director circle of the parabola x² + 2y = 4x – 3 .

Let L be the point (t, 2) and M be a point on the y-axis such that the slope of LM is −t. Then, the locus of the midpoint of LM is a parabola whose latus rectum is

(a)  2

(b)   1/2

(c)   4

(d)  1/4

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.

If the line lx + my + n = 0 touches the parabola y² = 4ax, then

(a)   In = am

(b)  In² = am²

(c)  l²n = am²

(d)   In = am²

In general, three normals can be drawn through a point in the plane of a parabola to the curve.

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°