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  4. The length of chord intercepted on the line 2 x+y=2 by the parabola y2=4 x, is

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Q. The length of chord intercepted on the line $2 x+y=2$ by the parabola $y^2=4 x$, is

Conic Sections

Solution:

$(2-2 x)^2=4 x \Rightarrow x^2-2 x+1=x$
$x^2-3 x+1=0 < _{x_2}^{x_1}$
$\left(x_1-x_2\right)^2=9-4=5$
similarly $\left(y_1-y_2\right)^2=20$
Length of chord $=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}=\sqrt{5+20}=5$