The equation of a parabola is 1/32 (y-2) 2=x-1.

What are the coordinates of the focus?

(1, 10)

(1, - 6)

(-7, 2)

(9, 2)

y = - 14x^2 - 2x - 2

We want to get to the form 4p (y - k) = (x - h) ^2

Where (h, k) is the vertex and p is the distance from the vertex to the focus

We can factor this as

y = - 14 [x^2 + (1/7) x + (1/7) ]

Complete the square inside the brackets

Take (1/2) of (1/7) = (1/14) ... square this = 1/196 ... add it and subtract it

So we have

y = - 14 [ x^2 + (1/7) x + 1/196 + (1/7) - (1/196) ]

Factor the first three terms and simplify the last two ... so we have

y = - 14 [ (x + 1/14) ^2 + 27/196] simplify

y = - 14 (x + 1/14) ^2 - 27/14 add 27/14 to both sides

(y + 27/14) = - 14 (x + 1/14) ^2 multiply both sides by - 1/14

(-1/14) (y + 27/14) = (x + 1/14) ^2

Since - 1/14 = 4p ... divide both sides by 4 ... then p = - 1/56

So ... the vertex is (h, k) = (-1/14, - 27/14)

And the focus is given by (h, k + p) =

(-1/14, - 27/14 - 1/56) =

( - 1/14, - 109/56)