Question

The coordinates of focus of parabola $9y^2-9x-12y-57=0$ is

• A. $(-\frac{235}{36},-\frac{2}{3})$
• B. $(-\frac{235}{36},\frac{2}{3})$
• C. $(\frac{235}{36},\frac{2}{3})$
• D. $(\frac{235}{36},-\frac{2}{3})$

Answer 1

The correct option is B $(-\frac{235}{36},\frac{2}{3})$

The given equation can be rewritten as ${(y-\frac{2}{3})}^2=(x+\frac{61}{9})$
which is of the form $Y^2=4AX$
$A=\frac{1}{4}$
Hence the vertex is $(-\frac{61}{9},\frac{2}{3})$
The axis is $y-\frac{2}{3}=0\Rightarrow y=\frac{2}{3}$
Focus
$=(-\frac{61}{9}+\frac{1}{4},\frac{2}{3})=(-\frac{235}{36},\frac{2}{3})$