Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]
How to find the equation of parabola with focus and directrix ?
We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]
So [tex]k+p=2[/tex]......(a)
And directrix of the parabola
[tex]y=k-p\\=-2[/tex]
[tex]k-p=-2[/tex]........(b)
So add the equation (a) AND (b)
[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]
Equation of the parabola with directrix and focus
[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]
Substitute all the values
[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]
Learn more about the equation of the parabola here:
https://brainly.com/question/28048848
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