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Question

The centre of a circle is (2a, a-7). Find the values of a if the circle passes through the point (11,-9) and has diameter 102 units.

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Solution

The length of the diameter is 102 units.
So, the radius is 52 units.
The centre of the circle be C(2a, a−7).
Suppose it passes through the point P(11, −9).
Therefore, PC = r
PC2=r211-2a2+-9-a+72=522121+4a2-44a+a2+4+4a=505a2-40a+75=0a-3a-5=0a=3 or a=5
Hence the values of a are 3 or 5.

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