Parabola
Normal Properties
Grade 11

Question:

<p>The locus of the middle point of 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 normal at two points lie on the original parabola to find midpoint locus.
<p>For chords where normals at both endpoints meet on the same parabola, eliminate parameters from the normal intersection condition and the parabola equation.</p><p>The locus is: \(y^4 - 4xy^2 + 4x^2 + 32y^2 - 96x + 64 = 0\)</p>
Correct Answer: s

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