Question

The equation of the circle whose centre is (1, –3) and which touches the line $2 x - y - 4 = 0$ is.

• A. $5 x ^ { 2 } + 5 y ^ { 2 } - 10 x + 30 y + 49 = 0$
• B. $5 x ^ { 2 } + 5 y ^ { 2 } + 10 x - 30 y + 49 = 0$
• C. $5 x ^ { 2 } + 5 y ^ { 2 } - 10 x + 30 y - 49 = 0$
• D. None of these

Answer 1

Answer: (A)

$5 x ^ { 2 } + 5 y ^ { 2 } - 10 x + 30 y + 49 = 0$

Answer 2

Radius of circle is $\left| \frac { 2 + 3 - 4 } { \sqrt { 5 } } \right| = \frac { 1 } { \sqrt { 5 } }$

Therefore, equation is $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = \frac { 1 } { 5 }$

or $x ^ { 2 } + y ^ { 2 } - 2 x + 6 y + 1 + 9 = \frac { 1 } { 5 }$

or $5 x ^ { 2 } + 5 y ^ { 2 } - 10 x + 30 y + 49 = 0$.