Show that the tangents at the ends of conjugate diameters of the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` intersect on the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=2`.

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

The locus of the point of intersection of tangents at the end-points of conjugate diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

If CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , then CP^(2) + CD^(2) =

The positive end of the Latusrectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b)" is

The locus of the point of intersection of the tangents at the extremities of the chords of the ellipse x^(2)+2y^(2)=6 which touch the ellipse x^(2)+4y^(2)=4, is x^(2)+y^(2)=4(b)x^(2)+y^(2)=6x^(2)+y^(2)=9(d) None of these

CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , The locus of the mid-point of PD, is

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1

the equation of a diameter conjugate to a diameter y=(b)/(a)x of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is