Explanation

(b)
Given, equation of ellipse is $\frac{x^{2}}{5/4} + \frac{y^{2}}{5/3} = 1$
Here, $a^{2} = \frac{5}{4},\ b^{2} = \frac{5}{3}$
Given, line is $y = 3x + 7$, whose slope is 3, therefore slopes of the parallel line is also 3
Now, equations of tangent are
$\Rightarrow \ y = mx \pm \sqrt{a^{2}m^{2} + b^{2}}$
$\Rightarrow y = 3x \pm \sqrt{\frac{5}{4}(3)^{2} + \frac{5}{3}}$
$\Rightarrow \ y = 3x \pm \sqrt{\frac{155}{12}}$