Question:
<p>The points on the parabola y<sup>2</sup> = 36x whose ordinate is three times the abscissa are</p>
<p style="display:inline">(4, 12) only</p>
<p style="display:inline">(1, 3), (4, 12)</p>
<p style="display:inline">(1, 1), (4, 12)</p>
<p style="display:inline">(0, 0), (4, 12)</p>
Step-by-Step Solution
Key Concept: Solve the system of equations formed by the parabola's equation and the linear constraint between the coordinates.
<p>Let the point be (x<sub>1</sub>, y<sub>1</sub>).<br />
y<sub>1</sub> = 3x<sub>1</sub> (Given)<br />
Substitute in y<sup>2</sup> = 36x to get<br />
<span class="math-tex">$\therefore$</span> <span class="math-tex">$9 x_{1}^{2}$</span> = 36x<sub>1</sub><br />
<span class="math-tex">$\Rightarrow$</span> x<sub>1</sub> = 4, 0<br />
<span class="math-tex">$\Rightarrow$</span> y<sub>1</sub> = 12, 0<br />
Hence, the points are (0, 0) and (4, 12).</p>
Correct Answer: D