A circle touches the parabola `y^2 =4ax` at P. It also passes through the focus S of the parabola and intersects its axis at Q. If angle SPQ is `90^@`, find the equation of the circle.

A circle cuts the parabola y^2=4ax at right angles and passes through the focus , show that its centre lies on the curve y^2(a+2x)=a(a+3x)^2 .

A circle cuts the parabola y^2=4ax at right angles and passes through the focus , show that its centre lies on the curve y^2(a+2x)=a(a+3x)^2 .

Let a circle touches to the directrix of a parabola y ^(2) = 2ax has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is

Let a circle touches to the directrix of a parabola y ^(2) = 2ax has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is

Through a point P (-2,0), tangerts PQ and PR are drawn to the parabola y^2 = 8x. Two circles each passing through the focus of the parabola and one touching at Q and other at R are drawn. Which of the following point(s) with respect to the triangle PQR lie(s) on the radical axis of the two circles?

If the line passing through the focus S of the parabola y=ax^(2)+bx+c meets the parabola at P and Q and if SP=4 and SQ=6, then find the value of a.

Find the radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and is also contained in it.

Find the radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and is also contained in it.