Question

The area of the circle having its centre at (3, 4) and touching the line $5x+12y-11=0$ is _____

• A. $16\pi sq.units$
• B. $4\pi sq.units$
• C. $12\pi sq.units$
• D. $25\pi sq.units$

Answer 1

The correct option is A $16\pi sq.units$

If line $5x+12y-11=0$ touches the circle, then

radius of the circle will be same as the distance of line from the center of the circle

$\Rightarrow r=|\frac{5\left(3\right)+12\left(4\right)-11}{\sqrt{5^2+{12}^2}}|=\frac{52}{13}=4$

Hence area of the circle is $=\pi (4{)}^2=16\pi$ sq. units