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From the point \left ( -1,2 \right ) tangent line are drawn the parabola \mathrm{y^{2}=4x}.find the area of triangle formed by chord of contact and tangent.

Option: 1

16


Option: 2

8


Option: 3

8\sqrt2


Option: 4

16\sqrt2


Answers (1)

Chord of contact of \mathrm{O(-1,2)\: is \\: : y y_1=2 a\left(x+x_1\right), or \: y=x-1}

Solving with parabola \mathrm{y^2=4 x}, we get the points

\mathrm{ P(3+2 \sqrt{2}, 2+2 \sqrt{2}), Q(3-2 \sqrt{2}, 2-2 \sqrt{2}) }

\mathrm{ \therefore P Q^2=32+32=64 }

\mathrm{ \therefore \quad P Q=8 }.Also if  \mathrm{ p } be perpendicular from  \mathrm{ O(-1,2)}  on
\mathrm{ \therefore P Q=8 }. Also if \mathrm{ p } be perpendicular from \mathrm{ O(-1,2)\: on\: P Q }, then area of triangle is
\mathrm{ \frac{1}{2} P Q \cdot P=\frac{1}{2} 8 \cdot\left(\frac{4}{\sqrt{2}}\right)=8 \sqrt{2} . }

Posted by

Ramraj Saini

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