Q83 / 160 · AP EAMCET 2009 · Mathematics

The area (in square unit) of the circle which touches the lines $4 x+3 y=15$ and $4 x+3 y=5$ is

  • A
    $4 \pi$
  • B
    $3 \pi$
  • C
    $2 \pi$
  • Correct answer
    D
    $\pi$

Solution

Since, given lines are parallel. $\begin{aligned} & \therefore \quad d=\frac{15-5}{\sqrt{4^2+3^2}}=\frac{10}{5} \\ & \Rightarrow \quad d=2=\text { diameter of the circle } \\ & \therefore \text { Radius of circle }=1 \\ & \therefore \text { Area of circle }=\pi r^2=\pi \text { sq unit } \end{aligned}$

Hence, the correct answer is option: 'D'.

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