Coordinate Geometry - Finding the Centre and Radius of a Circle
Coordinate Geometry - Finding the Centre and Radius of a Circle
TGM Original Questions
The line \(y + 3x = 6\) intersects the circle, \(C_{1}\), \(x^{2} + y^{2} - 2x - 4y = 11\) at \(A\) and \(B\).
- State the centre and find the radius of the circle.
- Find the coordinates of \(A\) and \(B\) and state if \(AB\) is the diameter of the circle.
- Find the equation of the circle \(C_{2}\), when \(C_{1}\) is reflected along the line \(x = 3\).
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Answer:(a) Centre \(=(1,2)\); Radius \(=4\) (b) \( (2.56, -1.68)\) (to \(3\) s.f.) and \((0.0390, 5.88)\) (to \(3\) s.f.); line segment \(AB\) is not a diameter (c) \( (x-5)^2 + (y-2)^2 = 16\)
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