Number of circles that can be drawn touching all the three lines $x + y - 2 = 0, 3 x + 4 y + 7 = 0$ and $2 x + 2 y - 3 = 0$

0

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Solution

The correct option is C $2$
$2 x + 2 y = 3$ can be written as $x + y = \frac{3}{2}$
$∴ x + y = 2$ & $2 x + 2 y = 3$ are two parallel lines.
$3 x + 4 y + 7 = 0$ cuts the parallel lines at only one point.
Clearly, from the figure
We can only draw two circles touching two parallel and one other lines.
Hence, the answer is $2$ .

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