A parabola is drawn to pass through A and B, the ends of a diameter of a given circle of radius a, and to have as directrix a tangent to a concentric circle of radius the axes of reference being AB and a perpendicular diameter, prove that the locus of the focus of parabola `x^2/a^2 + y^2/(b^2-a^2) = 1`

A parabola is drawn to pass through A and B the ends of a diameter of a given circle of radius a and to have as directrix a tangent to a concentric circle of radius b , the axes being AB and a perpendicular diameter. The locus of the focus of the parabola is a conic which is : (A) a parabola (B) an ellipse (C) a hyperbola which is not a rectangular hyperbola (D) a rectangular hyperbola

If the parabola y^(2)=ax passes through (1, 2) then the equation of the directrix is

The focal chords of the parabola y^(2)=16x which are tangent to the circle of radius r and centre (6, 0) are perpendicular, then the radius r of the circle is

A circle is drawn to pass through the extremities of the latus rectum of the parabola y^2=8xdot It is given that this circle also touches the directrix of the parabola. Find the radius of this circle.

A circle is drawn to pass through the extremities of the latus rectum of the parabola y^2=8xdot It is given that this circle also touches the directrix of the parabola. Find the radius of this circle.

The locus of foot of the perpendiculars drawn from the focus on a variable tangent to the parabola y^2 = 4ax is

Find the locus of the centre of the circle passing through the vertex and the mid-points of perpendicular chords from the vertex of the parabola y^2 =4ax .

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is

If one of the diameters of the circle x^2+y^2-2x-6y+ 6 = 0 is a chord to the circle with centre (2, 1), then the radius of circle is:

A variable chord is drawn through the origin to the circle x^2+y^2-2a x=0 . Find the locus of the center of the circle drawn on this chord as diameter.