Questions
The intercept on the line y = x by the circle is AB. The equation of the circle with AB as diameter, is
a
x2+y2+x+y=0
b
x2+y2=x+y
c
x2+y2−3x+y=0
d
none of these
detailed solution
Correct option is B
The equation of the circle passing through the intersect-ion of the circle x2+y2−2x=0 and the line (AB whose equation is y = x), is x2+y2−2x+λ(y−x)=0⇒x2+y2−x(2+λ)+λy=0Line y = x will be a diameter of this circle, if it passes throughthe centre 2+λ2,−λ2∴ −λ2=2+λ2⇒λ=−1.Putting λ=−1 in (i) we getx2+y2−x−y=0 as the equation of the required circleTalk to our academic expert!
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