Question

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

• A. 5
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (A)

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