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

Question

The equation of the circle passing through (2,0) and (0,4) and having the minimum radius, is (A) x2+y2=20 (B) x2+y2-2 x-4 y=0 (C) x2+y2=4 (D) x2+y2=16

Tardigrade Admin · Accepted Answer

For the minimum radius, required circle will be a circle on (2,0) and (0,4) as ends of diameter. ∴ Required equation of circle will be (x+2)(x-0)+(y-0)(y-4)=0 ⇒ x2+y2-2 x-4 y=0

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

$x^{2} + y^{2} = 20$

$x^{2} + y^{2} - 2 x - 4 y = 0$

$x^{2} + y^{2} = 4$

$x^{2} + y^{2} = 16$

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

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

x2+y2=20

x2+y2−2x−4y=0

x2+y2=4

x2+y2=16