1. ## Hyperbolas

Find the standard form of the equation of the hyperbola with the given characteristics

Vertices: (3,0), (3,-6)
asymptotes: y=x, y=4-x

Hello ryno16
Originally Posted by ryno16
Find the standard form of the equation of the hyperbola with the given characteristics

Vertices: (3,0), (3,-6)
asymptotes: y=x, y=4-x
Please check that you have given us the correct information here.

The given asymptotes meet at $\displaystyle (2,2)$. This is therefore the centre of the hyperbola. The hyperbola's axes are the lines $\displaystyle x = 2$ and $\displaystyle y = 2$, and the vertices should therefore be on one or other of these lines.