Question

If the equation \[ x+2y=3 \] represents the chord \(AB\) of the circle \[ x^2+y^2-4y=0, \] then the equation of the circle with \(AB\) as diameter is:

• A. \(2x^2+2y^2+5x+2y-15=0\)
• B. \(2x^2+2y^2-5x-18y+15=0\)
• C. \(5x^2+5y^2-2x-24y+6=0\)
• D. \(5x^2+5y^2+2x-16y-6=0\)

Hint:

Whenever a circle has a known diameter joining points \(A(x_1,y_1)\) and \(B(x_2,y_2)\), the fastest formula is \[ (x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0. \] It directly gives the required circle without first finding the centre and radius.

Answer 1

The Correct Option is D