Question

If the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` is inscribed in a rectangle whose length to breadth ratio is `2:1` , then the area of the rectangle is `4.(a^2+b^2)/7` (b) `4.(a^2+b^2)/3` `12.(a^2+b^2)/5` (d) `8.(a^2+b^2)/5`
A. `4*(a^(2)+b^(2))/(7)`
B. `4*(a^(2)+b^(2))/(3)`
C. `12*(a^(2)+b^(2))/(5)`
D. `8*(a^(2)+b^(2))/(5)`

Answer 1

Since mutually perpendicualar tangents can be drawn from the vartices of the reactangle , all the vertices of the rectangle should lie on the director circle `x^(2)+y^(2)=a^(2)+b^(2)`

Let breadht =2l and length =4l . then,
`l^(2)+(2l)^(2)=a^(2)+b^(2)`
or `l^(2)=(a^(2)+b^(2))/(5)`
or Area of `4lxx2l=8((a^(2)+b^(2))/(5))`