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A parabola drawn on a coordinate plane has vertex (5,3) and focus (7,3) What is the value of a when the equation of the parabola is expressed in the form (y - k) = a (z - h)?

User Zzheng
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1 Answer

14 votes
14 votes

Answer:

The equation of the parabola is;


(y-3)^2=8(x-5)

Step-by-step explanation:

Given the vertex;


(h,k)=(5,3)

and focus;


(h+a,k)=(7,3)

From the coordinates of the focus and the vertex we can observe that the focus and the vertex are on the same y-cordinates which means that they are on the same horizontal line.

So, the line of symmetry is perpendicular to the y axis and the parabola is an horizontal parabola.

The equation of the horizontal parabola can be derived using the equation;


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

Given;


\begin{gathered} h=5 \\ k=3 \\ h+a=7 \\ a=7-h=7-5 \\ a=2 \end{gathered}

Substituting the values;


\begin{gathered} (y-k)^2=4a(x-h) \\ (y-3)^2=4(2)(x-5) \\ (y-3)^2=8(x-5) \end{gathered}

Therefore, the equation of the parabola is;


(y-3)^2=8(x-5)
User J Cena
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