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TS EAMCET · Maths · Circle

The locus of the centre of the circles passing through the origin and cutting off a chord of length 2 units on the line x=1 is

  1. A a straight line
  2. B a circle
  3. C a parabola
  4. D on ellipse
Verified Solution

Answer & Solution

Correct Answer

(C) a parabola

Step-by-step Solution

Detailed explanation

Let centre of circle be h,k. Therefore, the equation of circle is x-h2+y-k2=h2+k22 ⇒x2+y2-2hx-2ky=0 CN=h-112+02=h-1 & PN=1 Also, CP2=CN2+PN2, using Pythagoras Theorem where CP is radius of the circle. ⇒h2+k2=h2-2h+1+1 ⇒k2=2-2h ⇒y2=21-x, which is a…