Conic Sections Question 415
Question: The equation of the ellipse whose centre is (2, -3), one of the foci is (3, -3) and the corresponding vertex is (4, -3) is
Options:
A) $ \frac{{{(x-2)}^{2}}}{3}+\frac{{{(y+3)}^{2}}}{4}=1 $
B) $ \frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1 $
C) $ \frac{x^{2}}{3}+\frac{y^{2}}{4}=1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Foci $ =(3,-3) $
therefore $ ae=3-2=1 $
Vertex $ =(4,-3) $
therefore $ a=4-2=2 $
therefore $ e=\frac{1}{2} $
therefore $ b=a\sqrt{( 1-\frac{1}{4} )}=\frac{2}{2}\sqrt{3}=\sqrt{3} $
Therefore, equation of ellipse with centre $ (2,-3) $ is $ \frac{{{(x-2)}^{2}}}{4}+\frac{{{(y+3)}^{2}}}{3}=1 $ .
BETA
