Question

The equation of the circle which passes through $(1,2)$ and $(0,2)$ and has its radius as small as possible is

• A. $x^2+y^2-2x-3y-2=0$
• B. $x^2+y^2-x-4y+4=0$
• C. $x^2+y^2-3x+4=0$
• D. $x^2+y^2+x+2y+1=0$

Answer 1

The correct option is B $x^2+y^2-x-4y+4=0$

The radius will be minimum, if the given points are the end points of a diameter.
Equation of circle in diametric form is
$(x-1)(x-0)+(y-2)(y-2)=0\Rightarrow x^2-x+y^2-4y+4=0\therefore x^2+y^2-x-4y+4=0$