CircleHardBloom L3
Question
From $(3,4)$ chords are drawn to the circle $x^{2} + y^{2} - 4x = 0$. The locus of the mid points of the chords is:
Options
A.$x^{2} + y^{2} - 5x - 4y + 6 = 0$
B.$x^{2} + y^{2} + 5x - 4y + 6 = 0$
C.$x^{2} + y^{2} - 5x + 4y + 6 = 0$
D.$x^{2} + y^{2} - 5x - 4y - 6 = 0$
Solution
[Key Concept: Midpoints of chords from a fixed external point lie on a circle — set $T = S_{1}$.]
Locus is Arc of the circle with $OP$ as diameter intercepted by the given circle.i.e.,
$$(x - 2)(x - 3) + y(y - 4) = 0$$
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