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:

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

$(119/20, 3)$

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