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

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

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

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

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

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

The normals to the parabola y^(2)=4ax from the point (5a,2a) is/are

Find the length of focal chord of the parabola x^(2)=4y which touches the hyperbola x^(2)-4y^(2)=1 _________

If x+y=k is a normal to the parabola y^(2)=12x then it touches the parabola y^(2)=px then