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)`

Foot of the directrix of the parabola y^(2) = 4ax is the point

A circle is drawn having centre at C (0,2) and passing through focus (S) of the parabola y^2=8x , if radius (CS) intersects the parabola at point P, then

If the focus of a parabola is (0,-3) and its directrix is y=3, then its equation is

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 the normal to the parabola y^2=4ax at the point (at^2, 2at) cuts the parabola again at (aT^2, 2aT) then

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

Circles are described on any focal chords of a parabola as diameters touches its directrix

Consider a circle with its centre lying on the focus of the parabola, y^2=2px such that it touches the directrix of the parabola. Then a point of intersection of the circle & the parabola is:

Focus of parabola y = ax^(2) + bx + c is