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Finding Equation of Circle

In this last section, you will need to apply all that you have learnt in the previous sections to find the equation of the circle. As you've learnt, to find the equation of the circle, you must have the centre and the radius. However, only certain pieces of information are given to you, and you will need to use the information to find the radius and the centre of the circle. Here are some problem-solving tips.

1: SKETCH WHENEVER YOU CAN! When you sketch, it takes a major load off your brain to attempt to visualise, as you can see it for yourself once you've sketched.

2: Find lines that pass through the centre of the circle. They can be the following:
  • Perpendicular bisector of a chord (if you have two known points on the circle, you can do this.)
  • Radius/Diameter of the circle (tangent perpendicular to radius)
So long as you can find two unique lines, you can find the centre of the circle. Regardless, sketch the lines out on your diagram too! 3. Once you've found the centre, finding the radius is easy. Just use the length formula from the centre to any point on the circle.

Practice Questions