Question

Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.

Answer 1

According to the question, the circle passes through the origin.
Let the equation of the circle be

\[x^2 + y^2 - 2hx - 2ky = 0\]

The circle cuts off chords of lengths 4 and 6 on the positive sides of the x-axis and the y-axis, respectively.

∴ Centre = \[\left( \frac{4}{2}, \frac{6}{2} \right) = \left( 2, 3 \right) = \left( h, k \right)\]

\[\Rightarrow h = 2, k = 3\]

∴ Required equation: \[x^2 + y^2 + 2\left( - 2 \right)x + 2\left( - 3 \right)y = 0\]

\[\Rightarrow x^2 + y^2 - 4x - 6y = 0\]