Question

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

• A. 5x² + 3y² = 32
• B. 3x² + 5y² = 32
• C. 5x² – 3y²= 32
• D. 3x² + 5y² + 32 = 0

Answer 1

Answer: (B)

3x² + 5y² = 32

Answer 2

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1. Since it passes through (-3,1)and(2,-2) so$\frac{9}{a^{2}} + \frac{1}{b^{2}}$ = 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 3x² + 5y² = 32.

Trick: Since only equation of ellipse is 3x² + 5y² = 32 passes through (-3, 1) and (2, -2).Hence the result.