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Prove that the points (9, 7), (11, 3) lie on a circle with centre at origin. Find the equation of the circle.

Answer»

SOLUTION :Let A and B be two points lie on the circle whose CENTRE at (0, 0).
`THEREFORE abs(bar(AC)) = sqrt(9^2+7^2) = sqrt(81+49) = sqrt(130)`
`abs(bar(BC)) = sqrt(11^2+3^2) = sqrt(121+9)=sqrt(130)`
`therefore` The points A and B lie on the circle whose centre at (0, 0) and radius is `sqrt(130)`
Eqn. of the circle is `x^2+y^2 = 130`.


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