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

1 Answer
Jul 1, 2017

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

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

Explanation:

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

x = a(y-6)^2+1" [2]"x=a(y6)2+1 [2]

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

a = 1/(4f)a=14f

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

f = 2-1f=21

f = 1f=1

a = 1/(4(1))a=14(1)

a = 1/4a=14

Substitute this into equation [2]:

x = 1/4(y-6)^2+1" [3]"x=14(y6)2+1 [3]

Equation [3] is the answer.