Question

The equation of circle whose centre lies on $3 x - y - 4 = 0$and $x + 3 y + 2 = 0$ and has an area 154 square units is.

• A. $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y - 47 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y + 47 = 0$
• C. $x ^ { 2 } + y ^ { 2 } + 2 x - 2 y - 47 = 0$
• D. None of these

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } - 2 x + 2 y - 47 = 0$

Answer 2

Centre is $( 1 , - 1 )$ (point of intersection of two given lines) and $\pi r ^ { 2 } = 154 \Rightarrow r = 7$

$\therefore$ Equation of required circle is $( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 49$

$\Rightarrow$ $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y - 47 = 0$