The parabola `y^(2)=4x` cuts orthogonally the rectangular hyperbola `xy=c^(2)` then `c^(2)=`

Show that for rectangular hyperbola xy=c^(2)

A point P moves such that the chord of contact of the pair of tangents P on the parabola y^(2)=4ax touches the the rectangular hyperbola x^(2)-y^(2)=c^(2). Show that the locus of P is the ellipse (x^(2))/(c^(2))+(y^(2))/((2a)^(2))=1

Find the length of that focal chord of the parabola y^(2) = 4ax , which touches the rectangular hyperbola 2xy = a^(2) .

A normal to the parabola y^(2)=4ax with slope m touches the rectangular hyperbola x^(2)-y^(2)=a^(2) if

If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2) , then

The parametric form of rectangular hyperbola xy=c^(2)

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^(2)=4ax touches the rectangular hyperbola x^(2)-y^(2)=c^(2). Show that the locus of P is the ellipse (x^(2))/(c^(2))+(y^(2))/((2a)^(2))=1

The condition that a straight line with slope m will be normal to parabola y^(2)=4ax as well as a tangent to rectangular hyperbola x^(2)-y^(2)=a^(2) is

At the point of intersection of the rectangular hyperbola xy=c^(2) and the parabola y^(2)=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi, respectively with x-axis,then