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 length of latus rectum of the locus of focus of the parabola is: (A) `2(a-b^2/a)` (B) `2 b^2/a` (C) `b/a` (D) `2(b- a^2/b)`

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

The length of the latus rectum of the parabola y^2+8x-2y+17=0 is a. 2 b. 4 c. 8 d. 16

Length of the latus rectum of the parabola sqrt(x) +sqrt(y) = sqrt(a) is (a) a sqrt(2) (b) (a)/(sqrt(2)) (c) a (d) 2a

Find the axis, vertex, tangent at the vertex, focus, directrix and length of latus rectum of the parabola x^2 = - 16y .

Given a circle of radius r . Tangents are drawn from point A and B lying on one of its diameters which meet at a point P lying on another diameter perpendicular to the other diameter. The minimum area of the triangle PAB is : (A) r^2 (B) 2r^2 (C) pir^2 (D) r^2/2

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.

A circle is described whose centre is the vertex and whose diameter is three-quarters of the latus rectum of a parabola y^2=4ax . The common chord of the circle and parabola is

If the parabola y^(2)=4ax passes through the (4,-8) then find the length of latus rectum and the co-ordinates of focus.