Identify the center of the ellipse and the foci.
-$\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 1$
A) center: $( - 3,6 )$;
foci: $\left( - 3 + \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$ and $\left( - 3 - \frac { 4 \sqrt { 166 } } { 35 } , 6 \right)$
B) center: $( - 6,3 )$;
foci: $( - 6 + 4 \sqrt { 166 } , 3 )$ and $( - 6 - 4 \sqrt { 166 } , 3 )$
C) center: $( 6 , - 3 )$;
foci: $( 6 + 4 \sqrt { 166 } , - 3 )$ and $( 6 - 4 \sqrt { 166 } , - 3 )$
D) center: $( 3 , - 6 )$;
foci: $\left( 3 + \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$ and $\left( 3 - \frac { 4 \sqrt { 166 } } { 35 } , - 6 \right)$

Question

Quizplus · Accepted Answer

The center of the ellipse is given by the h and k values in the equation, which are (3, -6). The foci are calculated using the formula for an ellipse, and in this case, they are correctly positioned along the x-axis from the center, indicating option D is correct.

Identify the Center of the Ellipse and the Foci 25(x−3)2169+49(y+6)2225=1\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 116925(x−3)2​+22549(y+6)2​=1

Identify the Center of the Ellipse and the Foci $\frac { 25 ( x - 3 ) ^ { 2 } } { 169 } + \frac { 49 ( y + 6 ) ^ { 2 } } { 225 } = 1$