Coordinate Geometry - Finding the Centre and Radius of a Circle
Coordinate Geometry - Finding the Centre and Radius of a Circle
TGM Original Questions
The points \(A(7, 7)\) and \(B(-2, -5)\) are at the opposite ends of a diameter of a circle \(C_1\). Find the
- centre of the circle and the radius of the circle.
- equation of the circle.
- equation of the perpendicular bisector \(AB\).
The circle, \(C_1\), is reflected in the \(x\)-axis.
- Find the equation of the reflected circle, \(C_2\).
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Answer:(a) Centre \(= \left( \frac{5}{2}, 1 \right)\); Radius \(=\frac{15}{2}\) (b) \( \left(x - \frac{5}{2} \right)^2 + (y - 1)^2 = \frac{225}{4}\) (c) \(y = -\frac{3}{4}x + \frac{23}{8}\) (d) \( \left( x-\frac{5}{2} \right)^2 + (y + 1)^2 = \frac{225}{4} \)
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