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`

The normal to parabola y^(2) =4ax from the point (5a, -2a) are

Let L be a normal to the parabola y^2=4x dot If L passes through the point (9, 6), then L is given by (a) y-x+3=0 (b) y+3x-33=0 (c) y+x-15=0 (d) y-2x+12=0

Show that the equation of the chord of the parabola y^2 = 4ax through the points (x_1, y_1) and (x_2, y_2) on it is : (y-y_1) (y-y_2) = y^2 - 4ax

The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k) The centroid of triangle PQR lies on (A) x=0 (B) y=0 (C) x=-a (D) y=a

The normal to the curve x^2=4y passing (1,2) is (A) x + y = 3 (B) x y = 3 (C) x + y = 1 (D) x y = 1

The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) meet on which of the following lines? (A) x = 3 (B) y = 3 (C) x + y = 4 (D) none of these

The locus of centroid of triangle formed by a tangent to the parabola y^(2) = 36x with coordinate axes is (a) y^(2) =- 9x (b) y^(2) +3x = 0 (c) y^(2) = 3x (d) y^(2) = 9x

If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is (a)12 (b) -12 (c) 24 (d) -24

If a line x+ y =1 cut the parabola y^2 = 4ax in points A and B and normals drawn at A and B meet at C. The normals to the parabola from C other than above two meets the parabola in D, then point D is : (A) (a,a) (B) (2a,2a) (C) (3a,3a) (D) (4a,4a)

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