Find the Eccentricity of the conic. $$\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$$
A)
Eccentricity: $e = \frac { \sqrt { 84 } } { 4 }$
B)
Eccentricity: $e = \frac { \sqrt { 100 } } { 4 }$
C)
Eccentricity: $e = \frac { \sqrt { 84 } } { 100 }$
D)
Eccentricity: $e = \frac { 4 \sqrt { 84 } } { 84 }$
E)
Eccentricity: $e = \frac { \sqrt { 84 } } { 10 }$

Question

Find the Eccentricity of the conic. $$\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$$ 
A)
Eccentricity: $e = \frac { \sqrt { 84 } } { 4 }$
B)
Eccentricity: $e = \frac { \sqrt { 100 } } { 4 }$
C)
Eccentricity: $e = \frac { \sqrt { 84 } } { 100 }$
D)
Eccentricity: $e = \frac { 4 \sqrt { 84 } } { 84 }$
E)
Eccentricity: $e = \frac { \sqrt { 84 } } { 10 }$

Quizplus · Accepted Answer

The equation is in the standard form of an ellipse, $\frac { x ^ { 2 } } { b ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } } = 1$, where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. In this case, $a = 10$ and $b = 4$. The eccentricity of an ellipse is given by the formula $e = \sqrt { 1 - \frac { b ^ { 2 } } { a ^ { 2 } } }$. Substituting the values of $a$ and $b$, we get $e = \sqrt { 1 - \frac { 4 ^ { 2 } } { 10 ^ { 2 } } } = \sqrt { 1 - \frac { 16 } { 100 } } = \sqrt { \frac { 84 } { 100 } } = \frac { \sqrt { 84 } } { 10 }$.

Find the Eccentricity of the Conic x2100+y216=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1100x2​+16y2​=1

Find the Eccentricity of the Conic $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 16 } = 1$