Graph Ellipses Not Centered at the Origin
-$$\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$$
A) foci at $( 1,3 - 3 \sqrt { 3 } )$ and $( 1,3 + 3 \sqrt { 3 } )$
B) foci at $( 3,1 - 3 \sqrt { 3 } )$ and $( 3,1 + 3 \sqrt { 3 } )$
C) foci at $( - 1,3 - 3 \sqrt { 3 } )$ and $( - 1,3 + 3 \sqrt { 3 } )$
D) foci at $( 2,3 - 3 \sqrt { 3 } )$ and $( 2,3 + 3 \sqrt { 3 } )$

Question

Quizplus · Accepted Answer

The given ellipse equation is $\frac{(x-1)^2}{9} + \frac{(y-3)^2}{36} = 1$. The center of this ellipse is at $(1, 3)$. The major axis is along the y-axis because $b^2 = 36$ is larger than $a^2 = 9$, and the distance from the center to the foci along the major axis is $c = \sqrt{b^2 - a^2} = \sqrt{36 - 9} = \sqrt{27} = 3\sqrt{3}$. Therefore, the foci are at $(1, 3 \pm 3\sqrt{3})$.

Graph Ellipses Not Centered at the Origin - (x−1)29+(y−3)236=1\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 19(x−1)2​+36(y−3)2​=1

Graph Ellipses Not Centered at the Origin
- $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$