Question

The equation of the diameter of the circle $3(x^2+y^2)-2x+6y-9=0$ which is perpendicular to line $2x+3y=12$ is

• A. $3x-2y=3$
• B. $3x-2y+1=0$
• C. $3x-2y=9$
• D. none of these

Answer 1

The correct option is A $3x-2y=3$

The centre of the circle is $(\frac{1}{3},-1)$ . Given that the diameter is perpendicular to the line having slope $-\frac{2}{3}$. So, the diameter will be having a slope of $\frac{3}{2}.$
Hence the equation becomes $3x-2y=3$.