A tangent having slope of `-4/3` to the ellipse `(x^2)/(18)+(y^2)/(32)=1` intersects the major and minor axes at points `Aa n dB ,` respectively. If `C` is the center of the ellipse, then find area of triangle `A B Cdot`

Normal to the ellipse (x^2)/(64)+(y^2)/(49)=1 intersects the major and minor axes at Pa n dQ , respectively. Find the locus of the point dividing segment P Q in the ratio 2:1.

For the ellipse x^(2)+ 3y^(2) = a^(2) find the length of major and minor axis.

Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

If normal at any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

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

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

The ratio of the volumes generated by revolving the ellipse (x^(2))/( 9) + ( y^(2))/( 4) = 1 about major and minor axes is

Consider an ellipse E ,(x^2)/(a^2)+(y^2)/(b^2)=1 , centered at point O andhaving A Ba n dC D as its major and minor axes, respectively. If S_1 is one of the focus of the ellipse, the radius of the incircle of triangle O C S_1 is 1 unit, and O S_1=6 units, then the value of (a-b)/2 is_________

Volume of solid obtained by revolving the area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 about major and minor axes are in tha ratio……

P and Q are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is