Let P be any point on the circle x^2+y^2-2x-1=0 and C be its centre. Let AB be the chord of contact of P with respect to the circle x^2+y^2-2x=0. Then the locus of the circumcentre of the triangle CA…

Question

Let P be any point on the circle x^2+y^2-2x-1=0 and C be its centre. Let AB be the chord of contact of P with respect to the circle x^2+y^2-2x=0. Then the locus of the circumcentre of the triangle CAB is

Accepted Answer

Correct answer: A. (a) Let P be (1+ 2 cos ⁡ , 2 sin ⁡ ) ,r= 2 with centre C (1 ,0 ) Here, circumcentre of triangle ABC is midpoint of PC ⇒2h=1+ 2 cos ⁡ +1 and 2k= 2 sin ⁡ ⇒ [2 (h-1 ) ]^2+ (2k )^2=2 ⇒2 (h-1 )^2+k^2-1=0 ⇒2x^2+2y^2-4x+1=0

$Let P be any point on the circle x^{2} + y^{2} - 2 x - 1 = 0 and C be its centre. Let AB be the chord of contact of P with respect to the circle x^{2} + y^{2} - 2 x = 0 . Then the locus of the circumcentre of the triangle CAB is$

Solution

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