Write an equation for the ellipse.
-minor axis from $( - 7 , - 1 )$ to $( - 1 , - 1 )$; major axis from $( - 4 , - 7 )$ to $( - 4,5 )$
A) $\frac { ( x - 4 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 36 } = 1$
B) $\frac { ( x + 4 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 36 } = 1$
C) $\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y + 4 ) ^ { 2 } } { 36 } = 1$
D) $\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 36 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of both the major and minor axes. For the minor axis from $(-7, -1)$ to $(-1, -1)$, the midpoint (and thus the center of the ellipse) is $(-4, -1)$. For the major axis from $(-4, -7)$ to $(-4, 5)$, the midpoint is also $(-4, -1)$, confirming the center. The length of the major axis is 12 units (from -7 to 5), so the semi-major axis $a = 6$, giving $a^2 = 36$. The length of the minor axis is 6 units (from -7 to -1), so the semi-minor axis $b = 3$, giving $b^2 = 9$. The equation of the ellipse in the form $\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$, where $(h, k)$ is the center, is $\frac{(x+4)^2}{9} + \frac{(y+1)^2}{36} = 1$.

Write an Equation for the Ellipse (−7,−1)( - 7 , - 1 )(−7,−1)

Write an Equation for the Ellipse $( - 7 , - 1 )$