Prove that the chords of contact of pairs of perpendicular tangents to the ellipse `x^2/a^2+y^2/b^2=1` touch another fixed ellipse.

Prove that the chords of constant of perpendicular tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch another fixed ellipse (x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/((a^(2)+b^(2)))

The locus of the point of intersection of perpendicular tangents to the ellipse (x - 1)^2/16 + (y-2)^2/9= 1 is

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(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

Prove that chord of contact of the pair of tangents to the circle x^(2)+y^(2)=1 drawn from any point on the line 2x+y=4 passes through a fixed point.Also,find the coordinates of that point.

The locus of foot of perpendicular from focus of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to its tangents is