Question

If the line x+y=1 cuts a circle x2+y2=1 at two points then the distance between two points are

Answer 1

Answer:

$\sqrt{2}$

Step-by-step explanation:

the equation of the line can be rewritten as $y=1-x$

using this in the equation of the circle

$x^2+y^2=1\\x^2+(1-x)^2=1\\x^2+1-2x+x^2=1\\2x^2-2x=0\\2x(x-1)=0\\x_1 =1\;\;\;\;x_2=0$

at $x=1$

$y=1-x=1-1=0\\(1,0)$

this is the first point and the second is

at $x=0$

$y=1-x=1-0=1\\(0,1)$

thus the distance

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{1^2+1^2}=\sqrt{2}$