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

Radius of the largest circle passing through the focus of the parabola y^2 = 4x and lying inside the parabola is…

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then

A circle whose centre is (4,-1) passes through the focus of the parabola x^2+16y=0 . Show that the circle touches the directrix of the parabola.

If a straight line passing through the focus of the parabola x ^(2) =4ay intersects the parabola at the points (x_(1) , y_(1)) and (x_(2), y_(2)) then the value of x_(1)x_(2) is-

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 a point of intersection of the circle & the parabola is:

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: