Question:
<p>The equation of the transverse and conjugate axis of the hyperbola 16x<sup>2 </sup>− y<sup>2 </sup>+ 64x + 4y + 44 = 0 are:</p>
<p style="display:inline">x = 3, y + 2 = 0</p>
<p style="display:inline">x = 2, y + 2 = 0</p>
<p style="display:inline">x = 4, y + 2 = 0</p>
<p style="display:inline">x = 2, y = 2</p>
Step-by-Step Solution
Key Concept: Complete the square for the x and y terms to transform the general quadratic into standard form, which allows for direct identification of the center and axes.
<p>(4x + 8)<sup>2</sup> - (y - 2)<sup>2</sup> = -44 + 64 - 4<br />
<span class="math-tex">$\Rightarrow$</span> <span class="math-tex">$\frac{16(x \ + \ 2)^{2}}{16}-\frac{(y \ - \ 2)^{2}}{16}$</span> = 1<br />
Transverse and conjugate axes are<br />
y = -2, x = 2</p>
Correct Answer: B