Graph Ellipses Not Centered at the Origin
-$25 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 900$
A) foci at $( - 2 + \sqrt { 11 } , 3 )$ and $( - 2 - \sqrt { 11 } , 3 )$
B) foci at $( 3 + \sqrt { 11 } , - 2 )$ and $( 3 - \sqrt { 11 } , - 2 )$
C) foci at $( - \sqrt { 11 } , 3 )$ and $( \sqrt { 11 } , 3 )$
D) foci at $( - 2 + \sqrt { 11 } , - 2 )$ and $( - 2 - \sqrt { 11 } , - 2 )$

Question

Quizplus · Accepted Answer

The given equation is in the form of an ellipse not centered at the origin. The center of the ellipse is at $(-2, 3)$. The foci are located along the major axis, which, based on the coefficients of the squared terms, is along the x-axis in this case. The distance from the center to each focus is $\sqrt{c^2} = \sqrt{a^2 - b^2}$, where $a^2 = 900/25 = 36$ and $b^2 = 900/36 = 25$, so $c = \sqrt{36 - 25} = \sqrt{11}$. Therefore, the foci are correctly given by $( - 2 + \sqrt { 11 } , 3 )$ and $( - 2 - \sqrt { 11 } , 3 )$.

Graph Ellipses Not Centered at the Origin - 25(x+2)2+36(y−3)2=90025 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 90025(x+2)2+36(y−3)2=900

Graph Ellipses Not Centered at the Origin
- $25 ( x + 2 ) ^ { 2 } + 36 ( y - 3 ) ^ { 2 } = 900$