Question

Find the equation of the circle whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it on y-axis.

Answer 1

It is given that the end points of the diameter of the circle are (−4, 3) and (12, −1).
∴ Required equation of circle: \[\left( x + 4 \right)\left( x - 12 \right) + \left( y - 3 \right)\left( y + 1 \right)\]

or

\[x^2 + y^2 - 8x - 2y - 51 = 0\]  ...(1)

Putting x = 0 in (1):
y² − 2y − 51 = 0
⇒ y² −  2y − 51 = 0
⇒ \[y = 1 \pm 2\sqrt{13}\]

Hence, the intercepts made by it on the y-axis is

\[1 + 2\sqrt{13} - 1 + 2\sqrt{13} = 4\sqrt{13}\]