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Q)

Find the equation to the chord of contact of tangents from the point $(-3 , 1 )$ to the parabola $y^{2}=8x$

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A)
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  • The chord of contact of tangents drawn from the point $(x_1,y_1)$ to the conic $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ is $Axx_1+\large\frac{B}{2}$$(xy_1+yx_1)+Cyy_1+D\large\frac{(x+x_1)}{2}+$$E\large\frac{(y+y_1)}{2}$$+F=0$
Step 1:
The equation of the chord of contact of tangents from $(x_1,y_1)$ is $yy_1=8\large\frac{(x+x_1)}{2}$
$\Rightarrow yy_1=4(x+x_1)$
Step 2:
Here $(x_1,y_1)=(-3,1)$
Therefore the equation is $y=4(x-3)$
$4x-y-12=0$
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