The area (in square unit) of the circle which touches the lines $4 x+3 y=15$ and $4 x+3 y=5$ is
The area (in square unit) of the circle which touches the lines $4 x+3 y=15$ and $4 x+3 y=5$ is
$4 \pi$
$3 \pi$
$2 \pi$
$\pi$
Solution
Since, given lines are parallel.
$\begin{aligned}
& \therefore \quad d=\frac{15-5}{\sqrt{4^2+3^2}}=\frac{10}{5} \\
& \Rightarrow \quad d=2=\text { diameter of the circle } \\
& \therefore \text { Radius of circle }=1 \\
& \therefore \text { Area of circle }=\pi r^2=\pi \text { sq unit }
\end{aligned}$