Question

If the centre of a circle \(S\) is \((2,4)\) and the length of the chord made by the secant \[ x+y+2=0 \] on \(S\) is \(6\) units, then the equation of the circle \(S\) is

• A. \[ x^2+y^2-4x-8y+21=0 \]
• B. \[ x^2+y^2+4x+8y+21=0 \]
• C. \[ x^2+y^2-4x-8y-21=0 \]
• D. \[ x^2+y^2+4x+8y-21=0 \]

Hint:

For a chord cut by a line at distance \(d\) from the centre, \[ \left(\frac{\text{Chord Length}}{2}\right)^2+d^2=r^2. \] First find the distance from the centre to the line, then compute the radius and form the circle equation.

Answer 1

The Correct Option is C