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

9.(i) Two tangents to a parabola y24ax meet at an angle of 45. Prove that the locus of their point of th guadrilntoral whose vortices lie at the pints of intersection of the parabola intersection is the curve y 2-4ax=(x+a)2

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

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

The direction cosines of a line which makes an angle of 45^(@) with Z-axis and congruent angles with X and Y axes, are

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

A variable chord of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1,(b>a), subtends a right angle at the center of the hyperbola if this chord touches.a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0,0).