Question

The locus of the mid point of the chord of the circle $x^2+y^2-2x-2y-2=0$ which makes an angle of ${120}^0$ at the centre is.

• A. $x^2+y^2-2x-2y+1=0$
• B. $x^2+y^2+x+y+1=0$
• C. $x^2+y^2-2x-2y+1=0$
• D. $x^2+y^2+x-y-1=0$

Answer 1

The correct option is A $x^2+y^2-2x-2y+1=0$

Given circle is $x^2+y^2-\phi -\phi -2=0Centre(1,1)Radius=2In\Delta OBPCos{60}^{\circ }=\frac{OP}{OB}OP=1(x-1{)}^2+(y-1{)}^2=1x^2+1+y^2-\phi +1=1x^2+y^2-2x-\phi +1=0$