What is the focus of the parabola #x + 5(y - 3)^2 = 6#?

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Answer 1 · 2016-10-23T02:24:20

#(119/20, 3)#

Write in vertex form for a left or right opening parabola, #x = a(y - k)^2 + h#:

#x = -5(y - 3)^2 + 6

The directed focal length, f, for all parabolas is:

#f = 1/(4a)#

Substitute -5 for a:

#f = 1/(4(-5))#

#f = -1/20#

The general form for the focus of a left or right opening parabola is:

#(h + f, k)#

Substitute 6 for h, 3 for k, and #-1/20# for f:

#(6 + -1/20, 3)#

#(119/20, 3)#