The equation of circle which touches the x- axis and y - axis at points (1, 0) and (0, 1) respectively, is

Question

The equation of circle which touches the x- axis and y - axis at points (1, 0) and (0, 1) respectively, is (A)  x2+y2-4y+3=0  (B)  x2+y2-2y-2=0  (C)  x2+y2-2x-27+2=0  (D)  x2+y2-2x-2y+1=0

Tardigrade Admin · Accepted Answer

Since, circle touches the x-axis and y-axis at points (1,0) and (0,1) respectively. So, centre of circle is (1,1) and radius is 1. Hence, equation of circle is (x-1)2+(y-1)2=12 ⇒ x2+y2-2x-2y+1=0

Q. The equation of circle which touches the $x -$ axis and $y$ - axis at points (1, 0) and (0, 1) respectively, is

$x^{2} + y^{2} - 4 y + 3 = 0$

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

$x^{2} + y^{2} - 2 x - 27 + 2 = 0$

$x^{2} + y^{2} - 2 x - 2 y + 1 = 0$

Since, circle touches the x-axis and y-axis at points (1,0) and (0,1) respectively.
So, centre of circle is (1,1) and radius is 1.
Hence, equation of circle is
$(x - 1)^{2} + (y - 1)^{2} = 1^{2}$
$\Rightarrow$ $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$

Q. The equation of circle which touches the x− axis and y - axis at points (1, 0) and (0, 1) respectively, is

x2+y2−4y+3=0

x2+y2−2y−2=0

x2+y2−2x−27+2=0

x2+y2−2x−2y+1=0