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The length of chord of contact of the tangents drawn from the point $(2,5)$ to the parabola $y^2=8 x$, is
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$\frac{3}{2} \sqrt{41}$
Equation of chord of contact of tangent drawn from a point $\left(x_1, y_1\right)$ to parabola $y^2=4 a x$ is $y y_1=2 a\left(x+x_1\right)$ so that $5 y=2 \times 2(x+2) \Rightarrow 5 y=4 x+8$. Point of intersection of chord of contact with parabola
$y^2=8 x$ are $\left(\frac{1}{2}, 2\right),(8,8)$, so that length $=\frac{3}{2} \sqrt{41}$
$y^2=8 x$ are $\left(\frac{1}{2}, 2\right),(8,8)$, so that length $=\frac{3}{2} \sqrt{41}$
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