The circle `x^2+y^2=5` meets the parabola `y^2=4x` at `P` and `Q` . Then the length `P Q` is equal to (A) 2 (B) `2sqrt(2)` (C) 4 (D) none of these

If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is (a)6 (b) 4 (c) 3 (d) none of these

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

The radius of the circle touching the parabola y^2=x at (1, 1) and having the directrix of y^2=x as its normal is (a)(5sqrt(5))/8 (b) (10sqrt(5))/3 (c)(5sqrt(5))/4 (d) none of these

If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR meet at A ,a n dS is the focus, then S PdotS qdotS R is equal to a^2S A (b) S A^3 (c) a S A^2 (d) none of these

If the circle x^2+y^2+2gx+2fy+c=0 is touched by y=x at P such that O P=6sqrt(2), then the value of c is (a)36 (b) 144 (c) 72 (d) none of these

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these