Conic Sections Question 178
Question: The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is
Options:
A) $ 5x^{2}+3y^{2}=32 $
B) $ 3x^{2}+5y^{2}=32 $
C) $ 5x^{2}-3y^{2}=32 $
D) $ 3x^{2}+5y^{2}+32=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \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} $
therefore $ a^{2}=\frac{32}{3} $ , $ b^{2}=\frac{32}{5} $
Hence required equation of ellipse is $ 3x^{2}+5y^{2}=32 $ .
Trick : Since only equation $ 3x^{2}+5y^{2}=32 $ passes through (-3, 1) and (2, -2).
Hence the result.
BETA
