Explanation

(a)
Let the equation of tangent which is perpendicular to the line $3x + 4y = 7,\ is\ 4x - 3y = \lambda \Rightarrow \ y = \frac{4}{3}x - \frac{\lambda}{3}$
Since, it is a tangent to the ellipse
$\therefore\left( \frac{\lambda}{3} \right)^{2} = 9 \times \left( \frac{4}{3} \right)^{2} + 4\ \ \ \lbrack\therefore a^{2} = 9,\ b^{2} = 4\rbrack$
$\Rightarrow \ \ \lambda^{2} = 180\ \Rightarrow \ \lambda = \pm 6\sqrt{5}$
$\therefore$ Equation is$\ 4x - 3y = \pm 6\sqrt{5}$