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 $10 \sqrt{2} u n i t s .$

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Solution

The distance of the centre of the circle from any point on the circle is the radius of the circle where the radius is half of the diameter.
Radius = $fraction numerator 10 square root of 2 over denominator 2 end fraction$ ---- (i)
Radius = ---- ii
From (i) and (ii)

= $fraction numerator 10 square root of 2 over denominator 2 end fraction$
Square both sides,

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