Q. The equation of an ellipse whose eccentricity is $\frac{1}{2}$ and the vertices are, (4,0) and (10, 0) is
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) $3x^{2} + 4y^{2} - 42x - 120 = 0$
Explanation
(a)
Major axis $= 6 = 2a$
$\Rightarrow \ a = 3$
Also , $e = \frac{1}{2}\ \ \Rightarrow \ b = \frac{3\sqrt{3}}{2}$
Thus required equation is
$\frac{(x - 7)^{2}}{9} + \frac{y^{2}}{\frac{27}{4}} = 1$
$\Rightarrow \ 3x^{2} + 4y^{2} - 42x + 120 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.