Question

The equation of the circle passing through the point (1,0) and (0,1) and having the smallest radius is.

Answer 1

We have,

$(x_1,y_1)=(1,0)$

$(x_2,y_2)=(0,1)$

Then,

Equation of circle is

$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$

$\Rightarrow (x-1)(x-0)+(y-0)(y-1)=0$

$\Rightarrow x(x-1)+y(y-1)=0$

$\Rightarrow x^2-x+y^2-y=0$

$\Rightarrow x^2+y^2-x-y=0$

Hence, this is the answer.