How do you find focus of a parabola #x=y^2 + 4#?

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Answer 1 · 2016-11-11T19:02:21

Please read the explanation.

The standard form for a parabola that opens left or right is

#x = ay^2 + by + c#

This matches the given equation

#x = y^2 + 4#

where #a = 1, b = 0 and c = 4#

To find the focus, you must begin by finding the vertex #(h, k)#

The formula for k of the standard form is:

#k = -b/(2a)#

But b is 0 in our equation:

#k = 0#

To find the value of h, evalaute the equation at #y = k = 0#:

#h = 0^2 + 4#

#h = 4#

The vertex is #(4, 0)#

For the standard form, the signed focal distance is

#f = 1/(4a)#

Because a = 1, the focal distance for our equation is:

#f = 1/4#

To obtain the focus, add the focal distance to the x coordinate of the vertex:

#(4.25, 0)#