What is the equation in standard form of the parabola

Heath Gilmore

Heath Gilmore

Answered question

2022-01-31

What is the equation in standard form of the parabola with a focus at (2,3) and a directrix of y= 9?

Answer & Explanation

lofia1r

lofia1r

Beginner2022-02-01Added 15 answers

Explanation:
for any point (x,y) on the parabola
the distance from (x,y) to the focus and directrix are equal
using the distance formula
with (x,y)(2,3)
(x2)2+(y3)2=|y9|
squaring both sides
(x2)2+(y3)2=(y9)2
x24x+4+y26y+9=y218y+81
x24x+12y68=0

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