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

A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&Q.

Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/4=1 touching the ellipse at point A and B. Q. The orthocenter of the trianlge PAB is

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

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Angle between tangents drawn from any point on the circle x^2 +y^2 = (a + b)^2 , to the ellipse x^2/a+y^2/b=(a+b) is-

If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes intercepts p and q on the coordinate axes, then a^(2)/p^(2) + b^(2)/q^(2) =

If a tangent of slope 1/3 of the ellipse (x^2)/a^2+y^2/b^2=1(a > b) is normal to the circle x^2 + y^2 + 2x + 2 y +1=0 then

A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P and Q. The angle between the tangents at P and Q of the ellipse x^2+2y^2=6 is

If a tangent to the ellipse x^2/a^2+y^2/b^2=1 , whose centre is C, meets the major and the minor axes at P and Q respectively then a^2/(CP^2)+b^2/(CQ^2) is equal to

From a point on the axis of x common tangents are drawn to the parabola the ellipse y^(2) =4x and the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(agtbgt0) . If these tangents from an equilateral trianlge with their chord of contact w.r.t parabola, then set of exhaustive values of a is