Coordinate Geometry - Finding the Centre and Radius of a Circle
Coordinate Geometry - Finding the Centre and Radius of a Circle
The points \(A(7,-6)\), \(B\left( 9,2 \right)\) and \(C\left( 1,4 \right)\) lie on a circle as shown in the diagram.
- Find the gradients of \(AB\) and \(BC\) and show that \(AC\) is the diameter of the circle.
- Find the coordinates of the centre of the circle and find the radius of the circle.
- Find the equation of the circle.
- Find the equation of the perpendicular bisector of \(BC\) and determine whether it passes through the centre of the circle.
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Answer:(a) \(m_{AB}=4\), \(m_{BC}=-\frac14\), so \(AC\) is the diameter (b) Centre \((4,-1)\), radius \(\sqrt{34}\) (c) \((x-4)^2+(y+1)^2=34\) (d) \(y=4x-17\), which passes through the centre
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