Question

The length of the chord x+y=3 intercepted by the circle x²+y²-2x-2y-2=0 is

• A. \(\dfrac{7}{2}\)
• B. \(\dfrac{3\sqrt{3}}{2}\)
• C. \(\sqrt{14}\)
• D. dfrac√(7)2

Hint:

Chord length =2√(r²-d²), where d is distance from centre.

Answer 1

The Correct Option is B

Centre of circle: (1,1), radius r=√(4)=2. Distance of centre from line x+y-3=0: d=frac|1+1-3|√(2)=\frac1√(2) Chord length: 2√(r²-d²) =2√(4-\frac12) =\frac3√(3)2