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.

The locus of the point of intersection of a pair of perpendicular tangents to an ellipse is a/an-

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

The locus of the point of intersection of two perpendicular tangents to the ellipse (x^(2))/(9) +(y^(2))/(4)=1 is -

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

The sum of the squares of the perpendiculars on any tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from two points on the minor axis each at a distance a e from the center is (a) 2a^2 (b) 2b^2 (c) a^2+b^2 (d) a^2-b^2

The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 forms a triangle of constant area with the coordinate axes is (a) straight line (b) a hyperbola (c) an ellipse (d) a circle

Prove that the chord of contact of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with respect to any point on the directrix is a focal chord.

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

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

If two points are taken on the minor axis of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^2dot