The angle between the tangents drawn to the parabola y2 = 12x from the point ( -3, 2 ) Option 1) $90^{\circ}$ Option 2) $60^{\circ}$ Option 3) $30^{\circ}$ Option 4) $45^{\circ}$

$T^{2}=SS_{1}$

$\Rightarrow \left ( 2y-6\left ( x-3 \right ) \right )^{2}=\left ( y^{2} -12x\right )\left ( 40 \right )$

$\Rightarrow \left ( y-3x+9 \right )^{2}=10y^{2}-120x$

$\Rightarrow y^{2}+9x^{2}+81-6xy-54x+18y=10y^{2}-120x$

$\Rightarrow 9x^{3}-9y^{2}-6xy+66x+18y+81=0$

$\Rightarrow 3x^{2}-3y^{2}-2xy+11x+6y+27=0$

$\tan \Theta =\frac{2\sqrt{1^{2}+9}}{0} = N.D$

$\Theta =90^{0}$

Option 1)

$90^{\circ}$

This is correct option

Option 2)

$60^{\circ}$

This is incorrect option

Option 3)

$30^{\circ}$

This is incorrect option

Option 4)

$45^{\circ}$

This is incorrect option

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