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# Write an equation of the parabola with the given focus and vertex Focus :$-5,-3$ vertex $-5,-6$

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## Answer to a math question Write an equation of the parabola with the given focus and vertex Focus :$-5,-3$ vertex $-5,-6$

Maude
4.7
\begin{aligned} & \text{1. Determine which form of the parabola equation to use. Since the vertex and focus differ in the y-coordinate only, } \\ & \text{the parabola opens vertically \lparen upwards or downwards\rparen. We use the standard form }$x-h$^2=4p$y-k$ \\ & \text{2. Identify the vertex }$h,k$\text{ and the focus }$h,k+p$. \\ & \text{3. From the given data: }$h,k$=$-5,-6$\text{ and focus}=$-5,-3$ \\ & \text{4. Calculate }p \\ & k+p=-3 \\ & -6+p=-3 \\ & p=3\text{ \lparen focus is 3 units above the vertex, so p is negative since the parabola opens downwards\rparen} \\ & \text{4. Substitute the values into the standard form }$x-h$^2=4p$y-k$ \\ & $x-(-5$)^2=4$3$$y-(-6$) \\ & $x+5$^2=12$y+6$ \\ & \text{The equation of the parabola is }$x+5$^2=12$y+6$ \\ & \placeholder{}\end{aligned}

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