SOLUTION: Find an equation of the parabola with vertex at (2, -4) and directrix x = -5.

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Question 1164212: Find an equation of the parabola with vertex at (2, -4) and directrix x = -5.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
If you try sketching the description, find that focus is at (9,-4).
Parabola is points (x,y) equally distant from (-5,y) as from (9,-4).

%28x-9%29%5E2%2B%28y-%28-4%29%29%5E2=%28x-%28-5%29%29%5E2%2B%28y-y%29%5E2
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highlight%2828%28x-2%29=%28y%2B4%29%5E2%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Find an equation of the parabola with vertex at (2, -4) and directrix x = -5.
With the DIRECTRIX being “x = ?”, we will have a PARABOLA with a HORIZONTAL AXIS of SYMMETRY (h).

We use the formula for a PARABOLA with a HORIZONTAL AXIS of SYMMETRY: matrix%281%2C3%2C+%28y++-++k%29%5E2%2C+%22=%22%2C+4p%28x++-++h%29%29, where:

                                                                      Vertex is: (h, k) = (2, - 4), and

                                                                      Directrix is:	

matrix%281%2C3%2C+%28y+-+k%29%5E2%2C+%22=%22%2C+4p%28x+-+h%29%29

matrix%281%2C3%2C+%28y+-+-+4%29%5E2%2C+%22=%22%2C+4%287%29%28x+-+2%29%29 ----- Substituting - 4 for k, 7 for p, and 2 for h