Prove that area common to ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and its auxiliary circle `x^2+y^2=a^2` is equal to the area of another ellipse of semi-axis a and a-b.

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

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

The parametric equations of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 are _

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.

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' as the major axis. Find the maximum area of triangle A P A '

Calculated the area enclosed by the ellipse 4x^(2) +9y^(2) =36 and the x-axis

The tangent at the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , meets its auxiliary circle at two points whose join subtends a right angle at the centre, show that the eccentricity of the ellipse is given by, (1)/(e^(2))=1+sin^(2)theta