The point `A` on the parabola `y^2 = 4ax`, for which `|AC - AB|` is maximum where `B-=(0, a) and C-= (-a, 0)` is (A) `(a, 2a)` (B) `(4a, 4a)` (C) `(a, -2a)` (D) none of these

The point P on the parabola y^(2)=4ax for which | PR-PQ | is maximum, where R(-a, 0) and Q (0, a) are two points,

The point on the parabola x^2 = y + 2 , where tangent is perpendicular to the chord joining A-= (14, 2) and B-= (2, 4) (A) (-3, 7) (B) (3, 7) (C) (4, 14) (D) (2, 2)

The point on the parabola 4x=y^2 + 9-6y which is closest to the circle x^2 + y^2 - 10x - 10y + 49 = 0 is: (A) (9/4, 0) (B) (4, 11) (C) (1, 1) (D) none of these

A circle, with its centre at the focus of the parabola y^2 =4ax and touching its directrix, intersects the parabola at the point (A) (a, 2a) (B) (a,-2a) (C) (a/2, a) (D) (a/2, 2a)

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

If normals at two points A(x_1, y_1) and B(x_2, y_2) of the parabola y^2 = 4ax , intersect on the parabola, then y_1, 2sqrt(2)a, y_2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If tangents at A and B on the parabola y^2 = 4ax , intersect at point C , then ordinates of A, C and B are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

The normal to the parabola y^2 = -4ax from the point (5a, 2a) are (A) y=x-3a (B) y=-2x+12a (C) y=-3x+33a (D) y=x+3a

At what point on the parabola y^2=4x the normal makes equal angle with the axes? (A) (4,4) (B) (9,6) (C) (4,-4) (D) (1,+-2)