Parabola
Normals
Grade 11

Question:

<p>The locus of the middle point of the chords of parabola \(y^2 = 4x\) such that normals at their extremities meet on same parabola is</p>

Step-by-Step Solution

Key Concept: Use the condition that normals at chord endpoints meet on the parabola to derive the locus.
<p>When normals at endpoints of a chord meet on the parabola itself, the locus of midpoints satisfies \(y^4 - 4xy^2 + 4x^2 + 32y^2 - 96x + 64 = 0\).</p>
Correct Answer: s

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