Locus of P(x,y) is given by `x^3+y^3+3xy=1` where `(x,y) !=(-1,-1)`.The equation of circle touching the locus of P at (-1,2) and psssing through (1,-2) is given by

Equation of circle touching x+y-2=0 at (1,1) and passing through (2,-3) is

Equation of circle touching line 2x+y=3 at (1,1) and also passing through point (2,3) is

The equation of a circle which touches the line y = x at (1 , 1) and having y = x -3 as a normal, is

The equation of normal to the curve x^(2)+y^(2)+xy=3 at P(1,1) is

The equation of normal to the curve x^(2)+y^(2)-3x-y+2=0 at P(1,1) is

Equation of the smaller circle that touches the circle x^(2)+y^(2)=1 and passes through the point (4,3) is

Locus of the centre of the circle touching the line 3x + 4y + 1=0 and having radius equal to 5 units is

If x=2t+1, y=1-t^(2) where t in R is a variable,locus of the point P(x,y) is a parabola whose focus is given by

Let locus L of a variable point P(x,y) is x^(3)+y^(3)=1-3xy,x!=-1.A circle with center C_(1)(2,2) and radius r touches L at Q(a,b) and line x+y=c,(c!=1)atR(d,e), then

The locus of centre of circle which touches the circle x^(2)+y^(2)=1 and y- axis in 1 st quadrant is