Convert the equation to the standard form for an ellipse by completing the square on x and y.
-$$25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$$
A) $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

To convert the given equation to the standard form of an ellipse, complete the square for both x and y terms. For x: $25(x^2 - 4x)$ becomes $25((x-2)^2 - 4)$. For y: $16(y^2 + 6y)$ becomes $16((y+3)^2 - 9)$. Substitute back and simplify to get $\frac{(x-2)^2}{16} + \frac{(y+3)^2}{25} = 1$.

Convert the Equation to the Standard Form for an Ellipse 25x2+16y2−100x+96y−156=025 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 025x2+16y2−100x+96y−156=0

Convert the Equation to the Standard Form for an Ellipse $25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$