The area (in square units) of the circle whic | vedclass

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(D) The given lines are $4x + 3y - 15 = 0$ and $4x + 3y - 5 = 0$. Since the coefficients of $x$ and $y$ are the same,the lines are parallel.The distan

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$\pi$

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(D) The given lines are $4x + 3y - 15 = 0$ and $4x + 3y - 5 = 0$. Since the coefficients of $x$ and $y$ are the same,the lines are parallel.The distance $d$ between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by $d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}$.Here,$d = \frac{|-15 - (-5)|}{\sqrt{4^2 + 3^2}} = \frac{|-10|}{\sqrt{16 + 9}} = \frac{10}{5} = 2$.Since the circle touches both lines,its diameter is equal to the distance between the lines,so $2r = 2$,which implies $r = 1$.The area of the circle is $\pi r^2 = \pi(1)^2 = \pi 	ext{ square units}$.

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

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