Conic Sections Question 402
Question: The equation of an ellipse whose eccentricity is 1/2 and the vertices are (4, 0) and (10, 0) is
Options:
A) $ 3x^{2}+4y^{2}-42x+120=0 $
B) $ 3x^{2}+4y^{2}+42x+120=0 $
C) $ 3x^{2}+4y^{2}+42x-120=0 $
D) $ 3x^{2}+4y^{2}-42x-120=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Major axis $ =6=2a $
therefore $ a=3 $
$ e=\frac{1}{2} $
therefore $ b=3\sqrt{1-\frac{1}{4}}=\frac{3\sqrt{3}}{2} $ . Also centre is (7, 0) Equation is $ \frac{{{(x-7)}^{2}}}{9}+\frac{y^{2}}{(27/4)}=1 $
therefore $ 3x^{2}+4y^{2}-42x+120=0 $ .
BETA
