CAIE IGCSE Additional Math 8.1 circle equations

Use this circle-equations page to read centre and radius, form equations from diameters and test whether points lie inside a circle.

Exam points

Find the centre and radius from a circle equation in completed-square form.
Use a diameter's endpoints to form the equation of the circle exactly.
Substitute a point into the circle equation to decide whether it lies inside.

[Maximum number: 1]

Point A has coordinates (3,-1).
A circle has equation $(x-4)^{2}+(y+3)^{2}=5$ .

Show that A lies on the circumference of the circle.

$(3-4)^{2}+(-1+3)^{2}=5$

or showing that distance between point A and centre of circle = radius e.g.
$\sqrt{(3-4)^{2}+(-1+3)^{2}}=\sqrt{5}$

B1

Accept if x-coordinate substituted to find
y - coordinate

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8.1. Use circle equations question 1