Find the length of intercept made by the straight line $x+y=3$ with circle $x^2+y^2-2x-1=0$.
My Attempt:
Equation of circle.. $$x^2+y^2-2x-1=0$$ Comparing above equation with $$x^2+y^2+2gx+2fy+c=0$$
centre$=(-g,-f)$, $=(1,0)$.
Now, what should I.do next?
Calculating the distance from centre $(1,0)$ of circle to the line $x+y=3$,
$d=\frac{|1+0-3|}{\sqrt{1^2+1^2}}=\sqrt 2=$radius of circle.
The answer must be zero as the line $x+y=3$ touches your circle.