Question:
<p>The axis of the parabola 9y<sup>2</sup> - 16x - 12y - 57 = 0 is</p>
<p style="display:inline">y = 3</p>
<p style="display:inline">x + 3y = 3</p>
<p style="display:inline">3y = 2</p>
<p style="display:inline">2x = 3</p>
Step-by-Step Solution
Key Concept: Convert the general equation into standard form $(y-k)^2 = 4a(x-h)$ by completing the square to identify the axis as the line $y-k=0$.
<p>9y<sup>2</sup> - 16x - 12y - 57 = 0<br />
<span class="math-tex">$\Rightarrow\left(y-\frac{2}{3}\right)^{2}=\frac{16}{9}\left(x+\frac{61}{16}\right)$</span><br />
Put y - <span class="math-tex">$\frac{2}{3}$</span> = Y and x + <span class="math-tex">$\frac{61}{16}$</span> = X<br />
<span class="math-tex">$\Rightarrow Y^{2}=4\left(\frac{4}{9}\right) X$</span><br />
Axis of this parabola is Y = 0<br />
<span class="math-tex">$\Rightarrow$</span> y - <span class="math-tex">$\frac{2}{3}$</span> = 0 <span class="math-tex">$\Rightarrow$</span> 3y = 2</p>
Correct Answer: C