Question

The equation to the circle with centre (2, 1) and touching the line $3 x + 4 y = 5$ is .

• A. $x ^ { 2 } + y ^ { 2 } - 4 x - 2 y + 5 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 4 x - 2 y - 5 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 4 x - 2 y + 4 = 0$
• D. $x ^ { 2 } + y ^ { 2 } - 4 x - 2 y - 4 = 0$

Answer 1

Answer: (C)

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

Answer 2

Centre : (2, 1)

Radius is distance of point (2, 1) from $3 x + 4 y = 5$

i.e.,

∴ circle is $( x - 2 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$

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