Coordinate Geometry

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

  1. x2 + y2 + 2x + 2y = 47
  2. x2 + y2 + 2x - 2y = 47
  3. x2 + y2 - 2x + 2y = 62
  4. x2 + y2 - 2x + 2y = 47

Answer

πr2 = 154

r = 7 

For centre, on solving equation

2x - 3y = 5 & 3x - 4y = 7 or x = 1, y = 1 centre = (1, -1)

Equation of circle: (x - 1)2 + (y + 1)2 = 72

The correct option is D.