The line `x-y-1=0` meets the parabola `y^2 = 4x` at A and B. Normals at A and B meet at C. If D CD is normal at D, then the co-ordinates of D are

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 point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as

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

A normal drawn to the parabola y^2=4a x meets the curve again at Q such that the angle subtended by P Q at the vertex is 90^0dot Then the coordinates of P can be (a) (8a ,4sqrt(2)a) (b) (8a ,4a) (c) (2a ,-2sqrt(2)a) (d) (2a ,2sqrt(2)a)

The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) meet on which of the following lines?

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

If the normals from any point to the parabola y^2=4x cut the line x=2 at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Q and Q^(prime), then Q Q^(prime) is

Statement 1: The line a x+b y+c=0 is a normal to the parabola y^2=4a xdot Then the equation of the tangent at the foot of this normal is y=(b/a)x+((a^2)/b)dot Statement 2: The equation of normal at any point P(a t^2,2a t) to the parabola y^2 = 4ax is y=-t x+2a t+a t^3