The equation of the parabola in vertex form is
.
How to derive the equation of a hyperbola
According to the figure, a hyperbola with major axis parallel with y-axis is shown. The vertex form of the hyperbola is shown below:

Where:
- (h, k) - Coordinates of the vertex.
- a - Length of the major axis.
- b - Length of the minor axis.
And the asymptote equations are, respectively:

Then, the equation of the hyperbola is simplified:
y² - x² = a²
Finally, we find the length of the major axis based on the location of any of the two co-vertices:
4² - 0² = a²
a² = 4²
a = 2
And the equation of the hyperbola in vertex form is:
