Question:
<p>The normal at a point P on the parabola y<sup>2</sup> = 8x meet the x-axis in G. If S is the focus and the triangle SPG is equilateral then the abscissa of the point P is:</p>
<p style="display:inline">3</p>
<p style="display:inline">6</p>
<p style="display:inline"><span class="math-tex">\(\frac 23\)</span></p>
<p style="display:inline">2<span class="math-tex">\(\sqrt 3\)</span></p>
Step-by-Step Solution
Key Concept: Utilize the inherent parabolic property that the distance from the focus S to point P (focal distance) is always equal to the distance from S to the normal's x-intercept G, then equate this to PG.
<p>6</p>
Correct Answer: B