Circle 5 Question 15

15. From the origin chords are drawn to the circle (x−1)2+y2=1. The equation of the locus of the mid points of these chords is… .

(1985,2M)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 15. x2+y2−x=0

Solution:

  1. For the equation of circle x2+y2−2x=0. Let the mid-point of chords be (h,k).

∴ Equation of chord bisected at the point is S1=T.

∴h2+k2−2h=xh+yk−(x+h) which passes through (0,0).

⇒

∴ The required locus of a chord is x2+y2−x=0

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