question_answer

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     AIEEE  Solved  Paper-2003

A) \[{{x}^{2}}+{{y}^{2}}+2x-2y=62\]

B) \[{{x}^{2}}+{{y}^{2}}+2x-2y=47\]

C) \[{{x}^{2}}+{{y}^{2}}-2x+2y=47\]

D) \[{{x}^{2}}+{{y}^{2}}-2x+2y=62\]

Correct Answer: C

Solution :

The equation of circle, circle centre is at (A, k) and radius r is                     The equations of diameters of a circle are                                              ... (i) and                                    ... (ii) On solving Eqs. (i) and (ii), we get                     .  Coordinates of centre are (1, -1) and area of the circle                             Equation of the circle whose centre (1 ,-1) and radius 7 is