Question

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

(a) x² + y² + 2x – 2y = 47 

(b) x² + y² – 2x + 2y = 47 

(c) x 2 + y² – 2x + 2y = 62 

(d) x² + y² + 2x – 2y = 62.

Answer 1

(b) : Coordinate of centre may be (1, –1) or (–1, 1) but 1, –1 satisfies the given equations of diameter, so choices (a) and (d) are out of court. Again πR² = 154, R² = 49 ∴ R = 7 

∴ Required equation of circle be 

(x – 1) 2 + (y + 1) 2 = 49 

=> x² + y² – 2x + 2y = 47