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

User Yuen Tong
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1 Answer

5 votes

ANSWER:


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

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}

User Oleg Abrazhaev
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