Given that the slope of the tangent to a curve y=y(x) at any point (x, y) is 2 y x^2 . If the curve passes through the centre of the circle x^2+y^2-2 x-2 y=0 , then its equation is

Step-by-step solution

aligned & Equation of the given circle is & x^2+y^2-2 x-2 y=0 & x^2-2 x+1+y^2-2 y+1=2 & (x-1)^2+(y-1)^2=2 & Centre of the circle is (1,1) aligned Now, slope of the given tangent is 2 y x^2 i.e., d y ~d x = 2 y x^2 . Integrating on both sides, we get 1 y ~d y=2 x⁻² ~d x |y|= -2 x +c ...(i) At (1,1) , we get 1=-2+c c =2 Required equation is aligned & |y|= -2 x +2 & i.e., x |y|=2(x-1) aligned