What is the equation in standard form of the parabola

Dillan Gibbs

Dillan Gibbs

Answered question

2022-01-31

What is the equation in standard form of the parabola with a focus at (10,-9) and a directrix of y= -14?

Answer & Explanation

sazrelomi0s

sazrelomi0s

Beginner2022-02-01Added 13 answers

Explanation:
from the given focus (10, -9) and equation of directrix y=-14, calculate p
p=12(914)=52
calculate the vertex (h,k)
h=10 and k=9+(14)2=232
Vertex (h,k)=(10,232)
Use the vertex form
(xh)2=+4p(yk) positive 4p because it opens upward
(x10)2=4(52)(y232)
(x10)2=10(y+232)
x220x+100=10y+115
x220x15=10y
y=x2102x32
the graph of y=x2102x32 and the directrix y=-14

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