Question

Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3).

Answer 1

Center at (5,3) -- It must look like this: \((x+5)^{2}\;and\;(y+3)^{2}\)

Vertices in the y-direction. Now we have: \((y+3)^{2} - (x+5)^{2}\)

Vertices are 2 away. Now we have: \(\dfrac{(y+3)^{2}}{2^2} - (x+5)^{2}\)

CoVertices are 6 away. Now we have: \(\dfrac{(y+3)^{2}}{2^2} - \dfrac{(x+5)^{2}}{6^{2}}\)

How are we doing?