Explanation

(c)
Equation of tangent at (1,2) is
$3x + 4y = 5$
Joint equation of tangent is
$\left( 3x^{2} + 2y^{2} - 5 \right)(3 + 8 - 5) = (3x + 4y - 5)^{2}$
$\Rightarrow 9x^{2} - 4y^{2} - 24xy + 30x + 40y - 30 = 0$
Here, $a = 9,\ b = - 4,\ h = - 12,\ g = 15$
(Comparing it with $ax^{2} + by^{2} + 2hxy + 2gx + 2fy + c = 0)\$
$\theta = \tan^{- 1}\left( \frac{2\sqrt{144 + 36}}{5} \right)$
$= \tan^{- 1}\left( \frac{2.2.3\sqrt{5}}{5} \right)$
$\Rightarrow \ \theta = \tan^{- 1}\left( \frac{12}{\sqrt{5}} \right)$