Explanation

(b)
Given equation of curve is $3x^{2} - 4y^{2} = 72$
Since, the points (6, 3) and (6-3) lies on the curve.
At point $(6,\ 3)$
$d_{1} = \frac{3(6) + 2(3) - 1}{\sqrt{3^{3} + 2^{2}}} = \frac{23}{\sqrt{13}}$
At point $(6 - 3)$
$d_{2} = \frac{3(6) + 2( - 3) - 1}{\sqrt{3^{3} + 2^{2}}} = \frac{11}{\sqrt{13}}$
Here, $d_{2}\$is minimum$.$
Hence, the point $(6,\ - 3)$ is on the curve which is nearest to the given line