Question

How do you find the focus of a parabola with the equation x=4(y-2)^2 +3 ??

Answer 1

it means vertex right?

Answer 2

it means focus

Answer 3

you have to find the vertex yes :) but then measure from it up by "a"

Answer 4

y^2 = 4ax is the general setup for this where a is the distance we seek

Answer 5

(x-3) = 4(y-2)^2

x = 4y^2

1/4 x = y^2

4a = 1/4 ; a = 1/8

Answer 6

since our vertex is at 3,2 ; and we open up to right; is say the focus is at (3+1/8 , 2)

Answer 7

i think my a is off

http://www.wolframalpha.com/input/?i=%28x-3%29+%3D+4%28y-2%29%5E2

Answer 8

a = 1/16 :)

Answer 9

thats better; (3+1/16, 2)

Answer 10

the key tho is to know the geometric eq for the parabola ....

Answer 11

Thank you! This was really helpful!

Answer 12

yw