Question

The axis of the parabola $9y^2-16x-12y-57=0$ is?

• A. $3y=2$
• B. $x+3y=3$
• C. $2x=3$
• D. $y=3$

Answer 1

The correct option is A $3y=2$

Since, $9y^2-16x-12y-57=0$
$\Rightarrow {(y-\frac{2}{3})}^2=\frac{16}{9}(x+\frac{61}{16})$
Put $y-\frac{2}{3}=y$ and $x+\frac{61}{16}=x$
$\Rightarrow y^2=4\left(\frac{4}{9}\right)x$
Axis of this parabola is $y=0$
$\Rightarrow y-\frac{2}{3}=0\Rightarrow y=\frac{2}{3}$
$\Rightarrow 3y=2$.