If the line passing through the focus `S` of the parabola `y=a x^2+b x+c` meets the parabola at `Pa n dQ` and if `S P=4` and `S Q=6` , then find the value of `adot`

The focus of the parabola y^2 = 20 x is

The focus of the parabola x^2 -2x +8y + 17=0 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 -1 1 m in R (d) none of these

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

If y=x+2 is normal to the parabola y^2=4a x , then find the value of adot

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x, then prove that 2a=b^2

If the line x+y=a touches the parabola y=x-x^2, then find the value of adot

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

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot

If the parabola y^2 = ax passes through (3,2) then the focus is