Question

What is the focus of the parabola given by the equation x = 3(y – 1)^2 + 2?

Answer 1

I keep getting (1, 2&1/12) but its not in my answer choices?

Answer 2

get that equation into this form:
\(\large 4p(x-h)=(y-k)^2 \)
since this is a parabola that opens to the right, you must add "p" to the x-coordinate of the vertex to the parabola to get the focus.

Answer 3

\(\large x=3(y-1)^2+2 \)
\(\large x-2=3(y-1)^2 \)
\(\large \frac{1}{3}(x-2)=(y-1)^2 \)

so \(\large 4a=\frac{1}{3}\rightarrow a=\frac{1}{12} \)
so all you do is add \(\frac{1}{12} \) to the x-coordinate of the vertex