Let a circle C of radius 5 lie below the x -axis. The line L _ 1 =...

Plotting the diagram of given data, we get

Finding intersection point of $4x + 3y + 2 = 0$ and $3x - 4y - 11 = 0$ we get \left(1, - 2\right)$</p><p>Now finding the point$P$by parametric we get,<img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/e17bd253-2bc5-471e-9cbc-fbd6c20b85e4-image.png" style="width: 200px; height: 137px;" /></p><p>$\dfrac{x - 1}{cos\theta} = \dfrac{y + 2}{sin\theta} = \pm 5$</p><p>$y = - 2 + 5\left(- \dfrac{4}{5}\right) = - 6$</p><p>$x = 1 + 5\left(\dfrac{3}{5}\right) = 4$</p><p>Now finding distance of point$P$from line$5x - 12y + 51 = 0$$= \left|\dfrac{5\left(4\right) - 12\left(- 6\right) + 51}{13}\right|$

$= \left|\dfrac{20 + 72 + 51}{13}\right|$

$= \dfrac{143}{13} = 11