How do you find the focus, vertex, and directrix of #x = 3(y – 1)^2 + 2#?

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Answer 1 · 2016-10-03T15:35:19

The vertex is #(1, 2)#
The focus is #(1, 25/12)#
The equation of the directrix is: #x = 23/12#

The given equation is in the vertex form of a parabola that opens either to the left or right:

#x = 1/(4f)(y - k)² + h#

where (h, k) is the vertex and f is the distance from the vertex to the focus.

The vertex is #(1, 2)#

The focus has the same x coordinate as the vertex but the y coordinate is increased by distance f:

#3 = 1/(4f)#

#f = 1/12#

The focus is #(1, 25/12)#

The directrix is a vertical line with perpendicular distance -f from the vertex:

The equation of the directrix is: #x = 23/12#