Question

If the line $3x-4y-8=0$ divides the circumference of the circle with centre $(2,-3)$ in the ratio $1:2$. Then, the radius of the circle is:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$3x-4y-8=0,(2,-3)$ centre of circle

radius of a circle $=\frac{3\times 2-4\times (-3)-8}{\sqrt{3^2+(-4{)}^2}}=\frac{6+12-8}{\sqrt{9+16}}=\frac{10}{5}=2$

eqn of circle can be written as,

$(x-2{)}^2+(y+3{)}^2=(2{)}^2$

$x^2+4-4x+y^2+9+6y=4$

$x^2+y^2-4x+6y+9=0$