How do you find the equation of the parabola described: Vertex at (1,6), and focus at (2,6)?

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Answer 1 · 2017-07-01T21:10:30

Because the focus is to the right of the vertex the standard form is:

#x = a(y-k)^2+h" [1]"#

Substitute the vertex #(1,6)# into equation [1]:

#x = a(y-6)^2+1" [2]"#

We can find the value of "a" using the formula:

#a = 1/(4f)#

Where is f is the signed horizontal distance from the vertex to the focus:

#f = 2-1#

#f = 1#

#a = 1/(4(1))#

#a = 1/4#

Substitute this into equation [2]:

#x = 1/4(y-6)^2+1" [3]"#

Equation [3] is the answer.