Question

An ellipse has the point (1, -1) and (2, -1) as its foci and x + y = 5 as one of its tangent then the value of $a^2+b^2$ where a, b are the lengths of semi major and semi minor axes of ellipse respectively, is

• A. $\frac{41}{2}$
• B. 10
• C. 19
• D. $\frac{81}{4}$

Answer 1

The correct option is D

$\frac{81}{4}$

$2ae=S{S}^1$
$=1p_1{p}_2=b^2$, where $p_1$ & $p_2$ are the length of perpendicular from S & $S^1$ to the tangent
$\frac{5}{\sqrt{2}}.\frac{4}{\sqrt{2}}=b^2\Rightarrow b^2\Rightarrow =10\Rightarrow b^2=10=a^2-e^2{a}^2\Rightarrow a^2=\frac{41}{4}\therefore a^2+b^2=\frac{81}{4}$