What is the equation of a parabola with a focus at (-2, 6) and a vertex at (-2, 9)?

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Answer 1 · 2017-09-05T06:12:16

#y=-x^2/12-x/3+26/3#

Given -

Vertex #(-2, 9)#
Focus #(-2,6)#

From the information, we can understand the parabola is in the second quadrant. Since focus lies below the vertex, The parabola is facing down.

The vertex is at #(h,k)#

Then the general form of the formula is -

#(x-h)^2=-4xxaxx(y-k)#

#a# is the distance between focus and vertex. It is #3#

Now substitute the values

#(x-(-2))^2=-4xx3xx(y-9)#
#(x+2)^2=-12(y-9)#

#x^2+4x+4=-12y+108#

By transpose we get -

#-12y+108=x^2+4x+4#

#-12y=x^2+4x+4-108#
#-12y=x^2+4x-104#

#y=-x^2/12-x/3+26/3#

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