Question

The equation of circle with centre (1, 2) and tangent $x + y - 5 = 0$is.

• A. $x ^ { 2 } + y ^ { 2 } + 2 x - 4 y + 6 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 2 x - 4 y + 3 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 8 = 0$
• D. $x ^ { 2 } + y ^ { 2 } - 2 x - 4 y + 8 = 0$

Answer 1

Answer: (B)

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

Answer 2

$\bullet \bullet$ Radius of circle = perpendicular distance of tangent from the centre of circle

$\Rightarrow$ $r = \frac { 1 + 2 - 5 } { \sqrt { 1 + 1 } } = \sqrt { 2 }$

Hence the equation of required circle is

$( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = ( \sqrt { 2 } ) ^ { 2 }$ $\Rightarrow x ^ { 2 } + y ^ { 2 } - 2 x - 4 y + 3 = 0$