Question

What is an equation of a parabola with the given vertex and focus? Vertex: (-2,5); focus: (-2,6)

Answer 1

ANSWER:

$\left(x+2\right)^2=4\left(y-5\right)$

STEP-BY-STEP EXPLANATION:

We can see that the vertex and the focus have the same coordinate in x, therefore, the equation of the parabola has the following form:

$\left(x-h\right)^2=4p\left(y-k\right)$

Where (h, k) is the vertex and p is the focal length, which we calculate as follows:

$p=y_2-y_1=6-5=1$

Now, we replace the vertex and the equation would finally be:

$\begin{gathered} (x-(-2))^2=4\cdot1(y-5) \\ \\ \left(x+2\right)^2=4\left(y-5\right) \end{gathered}$