Write the equation of a parabola with vertex (-5,8) and directrix x=2. Show all of your work and put your equation in graphing/v
ertex form.
1 answer:
ANSWER
![{(y - 8)}^{2} = - 28(x + 5)](https://tex.z-dn.net/?f=%7B%28y%20-%208%29%7D%5E%7B2%7D%20%20%3D%20%20-%2028%28x%20%20%2B%205%29)
EXPLANATION
We want to write the equation of a parabola with vertex (-5,8) and directrix x=2.
The equation of the directrix tells us that, the axis of symmetry of the parabola is parallel to the x-axis.
This type of parabola has equation of the form:
![{(y - k)}^{2} = 4p(x - h)](https://tex.z-dn.net/?f=%20%7B%28y%20-%20k%29%7D%5E%7B2%7D%20%20%3D%204p%28x%20-%20h%29)
p is the focal length of the parabola.
![|p| = |2 - - 5| = 7](https://tex.z-dn.net/?f=%20%7Cp%7C%20%20%3D%20%20%7C2%20-%20%20-%205%7C%20%20%3D%207)
p=-7 because the parabola opens along the negative x-axis.
Hence the equation is
![{(y - 8)}^{2} = 4( - 7)(x - - 5)](https://tex.z-dn.net/?f=%20%7B%28y%20-%208%29%7D%5E%7B2%7D%20%20%3D%204%28%20-%207%29%28x%20-%20%20-%205%29)
![{(y - 8)}^{2} = - 28(x + 5)](https://tex.z-dn.net/?f=%20%7B%28y%20-%208%29%7D%5E%7B2%7D%20%20%3D%20%20-%2028%28x%20%20%2B%205%29)
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