Q58 / 120 · VITEEE 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

Given lines are parallel. $d=\frac{15-5}{\sqrt{4^{2}+3^{2}}}=\frac{10}{5}$ $\Rightarrow d=2=$ diameter of the circle $\therefore$ Radius of circle $=1$ $\therefore$ Area of circle $=\pi \mathrm{r}^{2}=\pi$ sq unit

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

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