If the equation represents a hyperbola, find the center, foci, and asymptotes. If the equation represents an ellipse, find the center, vertices, and foci. If the equation represents a circle, find the center and radius. If the equation represents a parabola, find the focus and directrix.
-$$x ^ { 2 } + y ^ { 2 } - 14 x + 18 y = - 114$$
A) (9, -7); r = 16
B) (-9, 7); r = 4
C) (7, -9); r = 4
D) (-7, 9); r = 16

Question

Quizplus · Accepted Answer

Completing the square gives us $(x-7)^2+(y+9)^2=289$, which is the equation of a circle with center $(7,-9)$ and radius $17$. Therefore, none of the choices provided are correct.

If the Equation Represents a Hyperbola, Find the Center, Foci x2+y2−14x+18y=−114x ^ { 2 } + y ^ { 2 } - 14 x + 18 y = - 114x2+y2−14x+18y=−114

If the Equation Represents a Hyperbola, Find the Center, Foci $x ^ { 2 } + y ^ { 2 } - 14 x + 18 y = - 114$