Show that the tangents drawn at those points of the ellipse `(x^(2))/(a)+(y^(2))/(b)=(a+b)`, where it is cut by any tangent to `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`, intersect at right angles.

If the tangents from the point (lambda,3) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 are at right angles then lambda is

Show that the equation of the tangent to the ellipse (x^(2))/(a^(2))+ (y^(2))/(b^(2)) = 1 " at " (x_(1), y_(1)) " is " ("xx"_(1))/(a^(2)) + ("yy"_(1))/(b^(2)) = 1

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 .

A tangent is drawn to the ellipse to cut the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and to cut the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 at the points P and Q. If the tangents are at right angles,then the value of ((a^(2))/(c^(2)))+((b^(2))/(d^(2))) is

Angle between the tangents drawn from point (4, 5) to the ellipse x^2/16 +y^2/25 =1 is

A tangent is drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to cut the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 at the points P and Q . If tangents at P and Q to the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect at right angle then prove that (a^(2))/(c^(2))+(b^(2))/(d^(2))=1

Tangents are drawn from the point P(3,4) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 touching the ellipse at points A and B.

The area between the latusne latus rectum and tangents drawn at the end points of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is