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10-2. Parabola, Ellipse, Hyperbola
normal
In an ellipse, its foci and ends of its major axis are equally spaced. If the length of its semi-minor axis is $2 \sqrt{2}$, then the length of its semi-major axis is
A
$4$
B
$2 \sqrt{3}$
C
$\sqrt{10}$
D
$3$
(KVPY-2014)
Solution
(d)
Given, in cllipse
$A^{\prime} S^{\prime}=S S^{\prime}=S A$
$\therefore \quad S S^{\prime} =\frac{1}{3} A A^{\prime}$
$\Rightarrow \quad 2 a e =\frac{1}{3}(2 a)$
$\Rightarrow \quad =\frac{1}{3}$
$\text { Also given, } b =2 \sqrt{2}$
$\Rightarrow \quad \frac{1}{9} =1-\frac{b^2}{a^2}$
$\Rightarrow \quad \frac{8}{a^2} =1-\frac{1}{9}=\frac{8}{9}$
$\Rightarrow \quad a^2 =9$
$\therefore \quad a =3$
Standard 11
Mathematics
