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.
-$$25 x ^ { 2 } + 4 y ^ { 2 } - 300 x - 40 y + 900 = 0$$
A) C: (6, 5); V: (8, 5), (4, 5); F: (11.4, 5), (0.6, 5)
B) C: (6, 5); V: (6, 10), (6, 0); F: (6, 9.6), (6, 0.4)
C) C: (6, 5); V: (11, 5), (1, 5); F: (10.6, 5), (1.4, 5)
D) C: (6,5); V: (6, 7), (6, 3); F: (6, 10.4), (6, -0.4)

Question

Quizplus · Accepted Answer

The given equation is an ellipse after completing the square for both x and y terms. The center is at (6, 5), vertices along the y-axis are (6, 10) and (6, 0), and the foci are (6, 9.6) and (6, 0.4), indicating option B is correct.

If the Equation Represents a Hyperbola, Find the Center, Foci 25x2+4y2−300x−40y+900=025 x ^ { 2 } + 4 y ^ { 2 } - 300 x - 40 y + 900 = 025x2+4y2−300x−40y+900=0

If the Equation Represents a Hyperbola, Find the Center, Foci $25 x ^ { 2 } + 4 y ^ { 2 } - 300 x - 40 y + 900 = 0$