The angle between the tangents drawn to the parabola \(y^{2}=12 x\) from the point \((-3,2)\) is

Let \(S=y^{2}-12 x\)
Equation of pair of tangents is
\[
\begin{gathered}
\mathrm{SS}_{1}=\mathrm{T}^{2} \\
\Rightarrow \quad \quad\left(\mathrm{y}^{2}-12 \mathrm{x}\right)\left[(2)^{2}-12(-3)\right] \\
=[\mathrm{y}(2)-6(\mathrm{x}-3)]^{2} \\
\Rightarrow \quad\left(\mathrm{y}^{2}-12 \mathrm{x}\right)(40)=4(\mathrm{y}-3 \mathrm{x}+9)^{2} \\
\Rightarrow 10 \mathrm{y}^{2}-120 \mathrm{x} \\
=\mathrm{y}^{2}+9 \mathrm{x}^{2}+81-6 \mathrm{yx}-54 \mathrm{x}+18 \mathrm{y} \\
\Rightarrow 9 \mathrm{x}^{2}-9 \mathrm{y}^{2}-6 \mathrm{xy}+66 \mathrm{x}+18 \mathrm{y}+81=0 \\
\text { Here, } \mathrm{a}=9, \mathrm{~b}=-9 \\
\therefore \quad \quad \mathrm{a}+\mathrm{b}=0
\end{gathered}
\]
Hence, angle between tangents is \(90^{\circ}\).