Find the standard form of the equation of the ellipse with the given characteristics. vertices: $( - 6 , - 8 ) , ( - 6,6 ) \quad$ minor axis of length: 10
A) $\frac { ( x - 6 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 49 } = 1$
B) $\frac { ( x + 6 ) ^ { 2 } } { 25 } + \frac { ( y + 1 ) ^ { 2 } } { 49 } = 1$
C) $\frac { ( x + 6 ) ^ { 2 } } { 49 } + \frac { ( y + 1 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x + 1 ) ^ { 2 } } { 49 } + \frac { ( y + 6 ) ^ { 2 } } { 25 } = 1$
E) $\frac { ( x - 1 ) ^ { 2 } } { 49 } + \frac { ( y - 6 ) ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The vertices indicate the major axis is vertical, centered at $(-6, -1)$ with a length of $14$ ($6 - (-8) = 14$), so $a=7$ and $a^2=49$. The minor axis length is $10$, so $b=5$ and $b^2=25$. The correct equation is $\frac{(x+6)^2}{25} + \frac{(y+1)^2}{49} = 1$.

Find the Standard Form of the Equation of the Ellipse (−6,−8),(−6,6)( - 6 , - 8 ) , ( - 6,6 ) \quad(−6,−8),(−6,6)

Find the Standard Form of the Equation of the Ellipse $( - 6 , - 8 ) , ( - 6,6 ) \quad$