Question:
<p>Consider the feet of the normals from (3, 5) to y<sup>2</sup> = 8x. The arithmetic mean of the ordinates of these points is</p>
<p style="display:inline">4</p>
<p style="display:inline"><span class="math-tex">\(\frac{23}{3}\)</span></p>
<p style="display:inline">0</p>
<p style="display:inline"><span class="math-tex">\(\frac{16}{3}\)</span></p>
Step-by-Step Solution
Key Concept: The sum of the ordinates of the feet of the three normals drawn from any point to a parabola y² = 4ax is always zero, meaning their arithmetic mean is zero.
<p>Three feet of the normals say A(t<sub>1</sub>), B(t<sub>2</sub>), C(t<sub>3</sub>) are conormal points.<br />
<span class="math-tex">$\Rightarrow$</span> t<sub>1</sub> + t<sub>2</sub> + t<sub>3</sub> = 0.<br />
A.M. of the ordinates <span class="math-tex">$=\frac{2 a t_{1}+2 a t_{2}+2 a t_{3}}{3}$</span> <span class="math-tex">$=\frac{2 a(0)}{3}$</span> = 0.</p>
Correct Answer: C