Provide an appropriate response.
-In the ellipse $\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$, what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?
A) Horizontal: $y = 9$; Vertical: $x = - 5$
B) Horizontal: $y = 5$; Vertical: $x = - 9$
C) Horizontal: $y = - 5$; Vertical: $x = 9$
D) Horizontal: $y = 5$; Vertical: $x = 9$

Question

Quizplus · Accepted Answer

The axes of symmetry for an ellipse are determined by its center, which is given by the coordinates $(h, k)$ in the general equation $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$. For the given ellipse $\frac{(y+5)^2}{36} + \frac{(x-9)^2}{16} = 1$, the center is at $(9, -5)$, making the horizontal axis of symmetry $y = -5$ and the vertical axis of symmetry $x = 9$.

Provide an Appropriate Response (y+5)236+(x−9)216=1\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 136(y+5)2​+16(x−9)2​=1

Provide an Appropriate Response $\frac { ( y + 5 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$