Question

The equation of circle whose two diameters are $2x-3y=5,$ $3x-2y=10$ and having perimeter $6\pi \text{cm},$ is

• A. $(x-1{)}^2+(y+4{)}^2=9$
• B. $(x+1{)}^2+(y-4{)}^2=9$
• C. $(x-4{)}^2+(y-1{)}^2=9$
• D. $(x+4{)}^2+(y+1{)}^2=9$

Answer 1

The correct option is C $(x-4{)}^2+(y-1{)}^2=9$

$2x-3y=5$ and $3x-2y=10$
Solving the diameter equations, we get
$x=4,y=1$
$\Rightarrow$ Centre $=C(4,1)$
Perimeter $=2\pi r\Rightarrow 6\pi =2\pi r$
$\therefore r=3$

Equation of required circle is,
$(x-4{)}^2+(y-1{)}^2=9$