Coordinate Geometry - Finding the Equation of a Circle
Coordinate Geometry - Finding the Equation of a Circle
A circle with centre \(C\) passes through points \(A\left( -1,7 \right)\) and \(B\left( 0,8 \right)\).
- Explain why the perpendicular bisector of \(AB\) will pass through \(C\).
- Given that \(C\) lies on the line \(y=2x-2\), show that \(C\) is \(\left( 3,4 \right)\).
- Hence find the equation of the circle.
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Answer:(a) Since \(CA=CB\), \(C\) lies on the perpendicular bisector of \(AB\) (b) \(C=(3,4)\) (c) \((x-3)^2+(y-4)^2=25\)
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