isi-entrance 2012 Q23

isi-entrance · India · solved Circles Circle Equation Derivation

Find the equation of the circle with $AB$ as diameter, where $A$ and $B$ are the intercepts of the line $2x + 3y = k$ on the coordinate axes.

$A = (k/2, 0)$, $B = (0, k/3)$. Centre $= (k/4, k/6)$, radius $= (k\sqrt{13})/12$. The equation of the circle is $x^2 + y^2 - \dfrac{kx}{2} - \dfrac{ky}{3} = 0$. (C)

Find the equation of the circle with $AB$ as diameter, where $A$ and $B$ are the intercepts of the line $2x + 3y = k$ on the coordinate axes.

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