Coordinate Geometry - Finding the Centre and Radius of a Circle
Coordinate Geometry - Finding the Centre and Radius of a Circle
TGM Original Questions
- Find the coordinates of the centre and the radius of the circle \(x^{2} + y^{2} - 4x - 8y - 5 = 0\).
- If the circle cuts the \(x\)-axis at \(P\) and \(Q\), find the equation of the perpendicular bisector of the line \(PQ\).
- Given that the line \(2y - 6x + 4 = 0\) intersects the circle at \(R\) and \(S\), find the coordinates of \(R\) and \(S\). Hence show that the line segment \(RS\) is a diameter of the circle.
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Answer:(a) Centre \((2,4)\), radius \(5\). (b) \(x=2\). (c) \(\left(2\pm\dfrac{\sqrt{10}}{2},4\pm\dfrac{3\sqrt{10}}{2}\right)\), with matching signs; midpoint is the centre, so \(RS\) is a diameter.
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