write the equation of the hyperbola. The transverse axis of the hyperbola lies on the line y=–3 and has length 6, and the conjugate axis lies on the line x=2 and has length 8.

Question

write the equation of the hyperbola. The transverse axis of the hyperbola lies on the line y=–3 and has length 6, and the conjugate axis lies on the line x=2 and has length 8.

Answer 1

center = (2,-3)

semi axes are 4 and 3

(x-2)^2/4^2 - (y+3)^2/3^2 = 1

9(x-2)^2 - 16(y+3)^2 = 144

9x^2 -36x - 16y^2-96y = -324