Challenging Questions

Mathematics – Compulsory Part

Learning Unit: Equations of circles

Question M0-13-07

The coordinates of \(A\) and \(B\) are \((x_1, y_1)\) and \((x_2, y_2)\) respectively. \(AB\) is the diameter of a circle. Using the following independent methods, show that the equation of this circle is given by:

\( (x – x_1)(x – x_2) + (y – y_1)(y – y_2) = 0 \)

1. Consider an arbitrary point \(P \, (x, y)\) of this circle and find the slopes of \(PA\) and \(PB\)…
2. Consider the centre and radius of this circle…

---

# More challenging questions will be updated

# Answer