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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If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11,-9) and has diameter $10 \sqrt{2}$ units will be:

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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√2 units.

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 = ---- (i) Radius = ---- ii From (i) and (ii) = Square both sides,

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