Questions
The equation of the circle on the common chord of the circles
and as diameter is ,
a
x2+y2=2ab(bx+ay)
b
x2+y2=bx+ay
c
a2+b2x2+y2=2ab(bx−ay)
d
a2+b2x2+y2=2(bx+ay)
detailed solution
Correct option is C
The equation of the common chord of the circles (x−a)2+y2=a2 and x2+(y+b)2=b2 ax+by=0The equation of the required circle is (x−a)2+y2−a2+λ(ax+by)=0⇒x2+y2+x(aλ−2a)+λby=0 (i)Since (i) is a diameter of circle (ii). ∴a−(aλ−2a)2+b−λ,b2=0⇒λ=2a2a2+b2Putting the value of A in (ii), the equation of the required circle is a2+b2x2+y2=2ab(bx−ay)Talk to our academic expert!
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