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. \(\dfrac{3\sqrt3}{2}\)
• C. \(\sqrt{14}\)
• D. (\sqrt7)/(2)

Hint:

Chord length =2√(r²-d²), where d is distance of center from the line.

Answer 1

The Correct Option is C

Step 1: Write circle in standard form: (x-1)²+(y-1)²=4 So center C(1,1), radius r=2.
Step 2: Distance of center from line x+y-3=0: d=frac|1+1-3|√(2)=(1)/(\sqrt2)
Step 3: Length of chord: 2√(r²-d²)=2√(4-\frac12)=√(14)