# How do you find the equation of the parabola described: Vertex at (1,6), and focus at (2,6)?

Jul 1, 2017

Because the focus is to the right of the vertex the standard form is:

$x = a {\left(y - k\right)}^{2} + h \text{ [1]}$

#### Explanation:

Substitute the vertex $\left(1 , 6\right)$ into equation [1]:

$x = a {\left(y - 6\right)}^{2} + 1 \text{ [2]}$

We can find the value of "a" using the formula:

$a = \frac{1}{4 f}$

Where is f is the signed horizontal distance from the vertex to the focus:

$f = 2 - 1$

$f = 1$

$a = \frac{1}{4 \left(1\right)}$

$a = \frac{1}{4}$

Substitute this into equation [2]:

$x = \frac{1}{4} {\left(y - 6\right)}^{2} + 1 \text{ [3]}$