If the ellipse x 2 a 2 − 3 + y 2 a + 4 = 1 is inscribed in a square of side length a √ 2 then a is Options: A . &nbsp4 B . &nbsp2 C . &nbsp1 D . &nbspNone of these

If the ellipse x2a2−3+y2a+4=1 is inscribed in a square of side length a&#

Question

If the ellipse

\frac{x^{2}}{a^{2} - 3} + \frac{y^{2}}{a + 4} = 1

is inscribed in a square of side length

a \sqrt{2}

then a is

Options:

A . 4

B . 2

C . 1

D . None of these

Answer: Option D
:
D
Sides of the square will be perpendicular tangents to the ellipse so, vertices of the square will lie on director circle. So diameter of director circle is

2 \sqrt{(a^{2} - 3) + (a + 4)} = \sqrt{2 a^{2} + 2 a^{2}} 2 \sqrt{a^{2} + a + 1} = 2 a \Rightarrow a = - 1 B u t f o r e l l i p s e a^{2} > 3 & a > - 4

So there is no value of a which satisfy both.

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