Two parabola have the same focus. If their directrices are the x-axis and the y-axis respectively, then the slope of their common chord is :

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

A line makes angles of 45^@ and 60^@ with the z-axis and the x-axis respectively. The angle made by it with y-axis is

A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis and a common tangent of slope 2 with the circle x^2+y^2=5 is (are) (a) x=10 (b) x=20 (c) x=-10 (d) x=-20

Statement 1: If the endpoints of two normal chords A Ba n dC D (normal at Aa n dC) of a parabola y^2=4a x are concyclic, then the tangents at Aa n dC will intersect on the axis of the parabola. Statement 2: If four points on the parabola y^2=4a x are concyclic, then the sum of their ordinates is zero.

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

From the differential equation of the family of parabolas with focus at the origin and axis of symmetry along the x-axis. Find the order and degree of the differential equation.

Let there be two parabolas y^2=4a x and y^2=-4b x (where a!=ba n da ,b >0) . Then find the locus of the middle points of the intercepts between the parabolas made on the lines parallel to the common axis.