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

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

BITSATBITSAT 2009

Solution:

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