Parabola
Points on Parabola
Grade 11
Question:
<p>Let P be a point on the parabola <span class='math'>y^2 = 12x</span> and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is <span class='math'>\frac{4}{3}</span>, then</p>
<p>(a) <span class='math'>PN = 4</span></p>
<p>(b) <span class='math'>MQ = \frac{1}{3}</span></p>
<p>(c) <span class='math'>MQ = 1</span></p>
<p>(d) <span class='math'>PN = 3</span></p>
Step-by-Step Solution
Key Concept: Use the parametric form of parabola and the given conditions about the perpendicular, mid-point, and parallel line to find PN.
<p>No solution provided in text.</p>
Correct Answer: D