The equation of the ellipse whose centre is at origin and which p… - Vidyadip

MCQ

The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is

A
$5 x^2+3 y^2=32$
✓
$3 x^2+5 y^2=32$
C
$5 x^2-3 y^2=32$
D
$3 x^2+5 y^2+32= 0$

✓

Answer

Correct option: B.

$3 x^2+5 y^2=32$

(B)
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Since, it passes through $(-3,1)$ and $(2,-2)$
$\therefore \quad \frac{9}{ a ^2}+\frac{1}{b^2}=1$ and $\frac{1}{ a ^2}+\frac{1}{b^2}=\frac{1}{4}$
$\Rightarrow a^2=\frac{32}{3}, b^2=\frac{32}{5}$
Hence, required equation of ellipse is $3 x^2+5 y^2=32$

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