Circle And System Of Circles Question 80
Question: The intercept on the line $ y=x $ by the circle $ x^{2}+y^{2}-2x=0 $ is AB, equation of the circle on AB as a diameter is
[AIEEE 2004]
Options:
A) $ x^{2}+y^{2}+x-y=0 $
B) $ x^{2}+y^{2}-x+y=0 $
C) $ x^{2}+y^{2}+x+y= $ 0
D) $ x^{2}+y^{2}-x-y=0 $
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Answer:
Correct Answer: D
Solution:
Given, circle is $ x^{2}+y^{2}-2x=0 $ ……(i) and line is $ y=x $ …..(ii) Putting $ y=x $ in (i), We get $ 2x^{2}-2x=0\Rightarrow x=0,,1 $ From (i), $ y=0 $ , 1 Let $ A=(0,,0) $ , $ B=(1,,1) $ Equation of required circle is $ (x-0),(x-1)+(y-0),(y-1)=0 $ or $ x^{2}+y^{2}-x-y=0 $ .
BETA
