Question

An ellipse passes through the points $(3,1)$ & $(2,2)$ & its principal axis are along the co-ordinate axes in order. Find its equation.

• A. $3x^2+5y^2=32$
• B. $5x^2+3y^2=32$
• C. $3x^2+5y^2=64$
• D. $5x^2+3y^2=64$

Answer 1

Answer: (A)

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

Let the ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Given it passes through $(3,1)$ and $(2,2)$
$\Rightarrow \frac{9}{a^2}+\frac{1}{b^2}=1$ (i)
and $\frac{4}{a^2}+\frac{4}{b^2}=1$ (ii)
Solving (i) and (ii) we get $a^2=\frac{32}{3},b^2=\frac{32}{5}$
Hence the ellipse is, $3x^2+5y^2=32.$