Question:
<p>The focal distance of a point on the parabola y<sup>2</sup> = 16x whose ordinate is twice the abscissa, is</p>
<p style="display:inline">12</p>
<p style="display:inline">8</p>
<p style="display:inline">6</p>
<p style="display:inline">10</p>
Step-by-Step Solution
Key Concept: The focal distance of any point (x, y) on the parabola y² = 4ax is given by the formula x + a.
<p>Let point be (h, k). But 2h = k, then k<sup>2</sup> = 16h <span class="math-tex">$\Rightarrow$</span> 4h<sup>2 </sup>= 16h <span class="math-tex">$\Rightarrow$</span> h = 0, h = 4 <span class="math-tex">$\Rightarrow$</span> k = 0, k = 8<br />
Points are (0, 0), (4, 8). Hence focal distances are respectively 0 + a = 4, 4 + 4 = 8. (<span class="math-tex">$\because$</span> a = 4)</p>
Correct Answer: B