Question

The length of the chord cut off by $y=2x+1$ from the circle $x^2+y^2=2$ is

• A. $8/7$
• B. $6/\sqrt{5}$
• C. $5/6$
• D. $3/8$

Answer 1

Answer: (B)

Intersection points of line and circle

$x^2+(2x+1{)}^2=25x^2+4x-1=0$
$x=\frac{-4\pm \sqrt{16+20}}{10}=\frac{-4\pm 6}{10}=-1,\frac{1}{5}y=-1,\frac{7}{5}$

Point of intersection are $(-1,-1)$ and $(\frac{1}{5},\frac{7}{5})$

Length of chord $=\sqrt{{(-1-\frac{1}{5})}^2+{(-1-\frac{7}{5})}^2}=\sqrt{{\left(\frac{6}{5}\right)}^2+{\left(\frac{12}{5}\right)}^2}=\left(\frac{6}{5}\right)\sqrt{1+2^2}=\frac{6}{\sqrt{5}}$