Question

The equation of the circle passing through $(2,0)$ and $(0,4)$ and having the minimum radius, is

• A. $x^{2}+y^{2}=20$
• B. $x^{2}+y^{2}-2 x-4 y=0$
• C. $x^{2}+y^{2}=4$
• D. $x^{2}+y^{2}=16$

Answer 1

Answer: (B)

For the minimum radius, required circle will be a
circle on $(2,0)$ and $(0,4)$ as ends of diameter.
$\therefore $ Required equation of circle will be
$(x+2)(x-0)+(y-0)(y-4)=0$
$\Rightarrow x^{2}+y^{2}-2 x-4 y=0$