Question

The lines $2 x - 3 y = 5$ and $3 x - 4 y = 7$ are the diameters of a circle of area 154 square units. The equation of the circle is.

• A. $x ^ { 2 } + y ^ { 2 } + 2 x - 2 y = 62$
• B. $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 47$
• C. $x ^ { 2 } + y ^ { 2 } + 2 x - 2 y = 47$
• D. $x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 62$

Answer 1

Answer: (B)

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

Answer 2

Centre of circle = Point of intersection of diameters

= (1, ­–1)

Now area $= 154 \Rightarrow \pi r ^ { 2 } = 154 \Rightarrow r = 7$

Hence the equation of required circle is

$( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 7 ^ { 2 } \Rightarrow x ^ { 2 } + y ^ { 2 } - 2 x + 2 y = 47$.