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}

 

Answers (1)

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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