Question
Question: From the origin chords are drawn to the circle (x – 1)<sup>2</sup> + y<sup>2</sup> = 1. The equatio...
From the origin chords are drawn to the circle
(x – 1)2 + y2 = 1. The equation of the locus of the mid point of these chords are-
A
x2 + y2 + x = 0
B
x2 + y2 – x = 0
C
x2 – y2 – x = 0
D
None of these
Answer
x2 + y2 – x = 0
Explanation
Solution
(x – 1)2 + y2 = 1 ...(1)
C1(1, 0); r1 = 1
Equation of chord AB ̃ T = S1
̃ hx + ky – (x + h) = h2 + k2 – 2h
Q chord AB is passing through the O(0, 0)
i.e. ̃ –h = h2 + k2 – 2h ̃ x2 + y2 – x = 0