How do you find the focus, vertex, and directrix of x=1/4y^2+2y-2x=14y2+2y−2?

1 Answer
Leland Adriano Alejandro
Feb 25, 2016

Focus (-5, -4)(−5,−4), and Vertex (-6, -4)(−6,−4) and Directrix x=-7x=−7

Explanation:

From the given x=1/4y^2+2y-2x=14y2+2y−2
Multiply by 4
4x=y^2+8y_84x=y2+8y8
Perform completing the square method
4x=y^2+8y+16-16-8=04x=y2+8y+16−16−8=0

4x=(y+4)^2-244x=(y+4)2−24
(y--4)^2=4(x+6)(y−−4)2=4(x+6)
(y--4)^2=4(x--6)(y−−4)2=4(x−−6)

it is now in the Vertex Form
p=1p=1
Focus (-5, -4)(−5,−4), and Vertex (-6, -4)(−6,−4) and Directrix x=-7x=−7
graph{(x-1/4y^2-2y+2)(1000000x+y+7(1000000))=0[-20,20,-10,10]}

God bless you ! I hope you find this useful.

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