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What is the equation of this parabola in standard form?

What is the equation of this parabola in standard form?-example-1
User M B
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The given information is:

- The vertex of the parabola is (6,2)

- The equation of its directrix is y=0

As the directrix is y=0, this means we have a vertical parabola.

The standard form of the equation of a vertical parabola is given by:


(x-h)^2=4p(y-k)

Where (h,k) is the vertex of the parabola, and p is given by the directrix equation:


y=k-p

Let's start by finding p:


\begin{gathered} (h,k)=(6,2) \\ h=6,k=2 \\ y=k-p \\ 0=2-p \\ \therefore p=2 \end{gathered}

Now, replace the known values and find the equation:


\begin{gathered} (x-6)^2=4*2*(y-2) \\ \therefore(x-6)^2=8(y-2) \end{gathered}

The answer is above.

User Samsin
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