Conic-Sections Question 545
Question: The length of the chord $ x+y=3 $ intercepted by the circle $ x^{2}+y^{2}-2x-2y-2=0 $ is
Options:
A) $ \frac{7}{2} $
B) $ \frac{3\sqrt{3}}{2} $
C) $ \sqrt{14} $
D) $ \frac{\sqrt{7}}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] The centre of the circle is $ C(1,1) $ and radius of the circle is 2, perpendicular distance from C on AB, the chord $ x+y=3 $ $ CD=| \frac{1+1-3}{\sqrt{2}} |=\frac{1}{\sqrt{2}} $
$ \therefore AD=\sqrt{4-\frac{1}{2}}=\sqrt{\frac{7}{2}} $ $ [AD=\sqrt{AC^{2}-CD^{2}}] $ Hence, the length of the chord $ AB=2AD=2\sqrt{\frac{7}{2}}=\sqrt{14} $
BETA
