Parabola
Chord Properties
Grade 11
Question:
<p><strong>Question 2:</strong> Locus of midpoints of chords of parabola, which subtend a right angle at vertex of parabola is:</p>
<p>(a) \(y^2 - 4x + 32 = 0\)</p>
<p>(b) \(y^2 + 4x - 32 = 0\)</p>
<p>(c) \(y^2 - 32x + 4 = 0\)</p>
<p>(d) \(y^2 + 32x - 4 = 0\)</p>
Step-by-Step Solution
Key Concept: Apply the perpendicularity condition at the vertex and use parametric form to find the locus of midpoints.
<p><strong>Solution:</strong> For a chord of the parabola that subtends a right angle at the vertex, use the condition that if chord endpoints are \((at_1^2, 2at_1)\) and \((at_2^2, 2at_2)\), then \(t_1 t_2 = -4\). The locus of midpoints is \(y^2 + 4x - 32 = 0\).</p>
Correct Answer: B