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Consider the following equation of a parabola.y2 - 4y = -4x - 8Step of 3: Find the focus of the parabola.

Consider the following equation of a parabola.y2 - 4y = -4x - 8Step of 3: Find the-example-1
User Jkatzer
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1 Answer

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Step-by-step explanation:

Given;

We are given the equation of a parabola as shown below;


y^2-4y=-4x-8

Required;

We are required to find the focus of the parabola.

Step-by-step solution;

We re-write this equation and express x in terms of y;


\begin{gathered} y^2-4y=-4x-8 \\ y^2-4y+8=-4x \\ Multiply\text{ all through by }-1: \end{gathered}
\begin{gathered} -y^2+4y-8=4x \\ Divide\text{ all through by 4:} \end{gathered}
(4x)/(4)=(1)/(4)(-y^2+4y-8)
x=-(1)/(4)(y^2-4y+8)

We now write this out in the vertex form which is;


\begin{gathered} x=a(y-b)^2+c \\ Where:vertex=(b,c) \end{gathered}

We now simplify the right side of the equation;


x=-(1)/(4)((y-2)^2-4+8)
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User Csabi
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