Please solve below problem and clearly state the answers Fin

Please solve below problem and clearly state the answers.

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. (y + 2)^2/25 - (x + 2)^2/4 = 1 vertices (x, y) = () (smaller y-value) (x, y) = () (larger y-value) foci (x, y) = () (smaller y-value) (x, y) = () (larger y-value) asymptotes (smaller slope) (larger slope) Sketch its graph, showing the asymptotes and the foci.

Solution

Equation of hyperbola is

[(y+2)^2/25] - [(x+2)^2/4] = 1

25x^2 100x + 4y^2 + 16y 184 = 0

Vertices: (2,7), (2,3)

Foci: (2,292) (2,7.3851648071345), (2,2+29) (2,3.3851648071345)

First asymptote: y = 5x/2 7 = 2.5x 7.0

Second asymptote: y = 5x/2 + 3 = 2.5x + 3.0