[" A normal to the parabola "y^(2)=4ax" with slope "n],[" touches the rectangular hyperbola "x^(2)-y^(2)=a^(2)" if "]

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

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

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

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

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

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

Equation of normal to the parabola y^(2)=4ax having slope m is

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

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

If a normal of slope m to the parabola y^(2)=4ax touches the hyperbola x^(2)-y^(2)=a^(2), then