Find the eccentricity of the ellipse.
-$144 x ^ { 2 } + y ^ { 2 } = 144$
A) $\frac { \sqrt { 143 } } { 12 }$
B) $\sqrt { 143 }$
C) $\sqrt { 145 }$
D) $\frac { \sqrt { 145 } } { 12 }$

Question

Quizplus · Accepted Answer

To find the eccentricity of an ellipse, we need to find its semi-major axis (denoted by a) and semi-minor axis (denoted by b). We can rewrite the given equation by dividing both sides by 144:
$\frac{ x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 12 ^ { 2 } } = 1$
Comparing with the standard form of the ellipse: 
$\frac{ x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$
We get:
$a ^ { 2 } =144 , \ b ^ { 2 } = 12 ^ { 2 }$
Hence,
$c = \sqrt {a^2 - b^2} = \sqrt{144-144/12^2}= \sqrt{143}$
The eccentricity, denoted by e, is given by:
$e = \frac { c } { a }$
substituting, we get:
$e = \frac { \sqrt { 143 } } { 12 }$

Find the Eccentricity of the Ellipse 144x2+y2=144144 x ^ { 2 } + y ^ { 2 } = 144144x2+y2=144

Find the Eccentricity of the Ellipse $144 x ^ { 2 } + y ^ { 2 } = 144$