Finding Standard for with a Vertex and a point?

Question

Ok math book k= Unhelpful

Determine the standard form of the equation of a hyperbola with vertices (2,0) and passing through (4,3)

So if anyone could even just get me started that would be fantastic!

Answer 1

The standard equation of hyperbola whose axis is the x-axis with vertex at (c,d):
(x-c)^2/a^2 - (y-d)^2/b^2 = 1

Here c = 2, d = 0

Substitute in the equation for c and d and get: (x-2)^2/a^2 - y^2/b^2 = 1

This hyperbola passes through (4,3).
So, x = 4 and y = 3 must satisfy the above equation.
(4-2)^2/a^2 - 3^2/b^2 = 1
4/a^2 - 9/b^2 = 1

You need another condition to find the values of a and b.