1. ## Ellipses standard form

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

Vertices: (-2,1),(2,1);
passes through the point (5,4)

2. The equation of a hyperbola is given by $\frac{(x-h)^2}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$, where $(h,k)$ is the centre of the hyperbola.

For your question, the centre of the hyperbola is $(0,1)$, and $a=2$ since $a$ is the distance from the vertices to the centre.

Thus, $\frac{(x-0)^2}{2^{2}}-\frac{(y-1)^{2}}{b^{2}}=1$

Since the curve passes through $(5,4)$, you can find $b^{2}$ by substitution.