question_answer

The straight line \[2x+3y-k=0,\] \[k>0\] cuts the x and y-axes at A and B. The area of \[\Delta OAB,\], where 0 is the origin, is \[12\text{ }sq\]unit.    The equation of the circle having AB as diameter is

A) \[{{x}^{2}}+{{y}^{2}}-6x-4y=0\]

B) \[{{x}^{2}}+{{y}^{2}}+4x-6y=0\]

C) \[{{x}^{2}}+{{y}^{2}}-6x+4y=0\]

D) \[{{x}^{2}}+{{y}^{2}}-4x-6y=0\]

Correct Answer: A

Solution :

Given, equation of line, \[2x+3y-k=0,\] \[k>0\] \[\Rightarrow \]               \[\frac{x}{\frac{k}{2}}+\frac{y}{\frac{k}{3}}=1\]