Two concentric hyperbolas, whose axes meet at angle of `45^@`, cut

The differential equation of rectangular hyperbolas whose axes are asymptotes of the hyperbola x^2 - y^2= a^2 , is :

The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola, is

Equation of the hyperbola whose axes are the axes of coordinates (focus lying on x-axis) and which passes through the point (-3, 1) and has eccentricity sqrt(3) can be

Find the equation of tangents to the hyperbola x^(2)-2y^(2)=8 that make an angle of 45^(@) with the positive direction of x -axis .

Find the equation of hyperbola : whose axes are coordinate axes and the distances of one of its vertices from the foci are 3 and 1

A ball whose kinetic energy is E , is projected at an angle of 45(@) to the horizontal . The kinetic energy of the ball at the highest point of its flight will be

Find the equation of the hyperbola whose transverse and conjugate axes are the x and y axes respectively, given that the length of conjugate axis is 5 and distance between the foci is 13.

Given the base of a triangle and the ratio of the tangent of half the base angles .Show that the vertex moves on a hyperbola whose foci are the extremities of a diameter

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

Find the equation of the hyperbola, referred to its axes as the axes of coordinates, Whose transverse and conjugate axes in length respectively 2 and 3,