The coordinates of the centre of a circle are (2a, a - 7) . Find the value(s) of ' a ' if the circle passes through…

CBSE Class 10 Maths PYQ · Coordinate Geometry · Application · 2 Marks · March 2025 · Standard

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1632 Marks · March 2025 · Standard
The coordinates of the centre of a circle are $(2a, a - 7)$. Find the value(s) of '$a$' if the circle passes through the point $(11, -9)$ and has diameter $10\sqrt{2}$ units.
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Radius $= 5\sqrt{2}$ units. $(2a - 11)^2 + (a - 7 + 9)^2 = 50 \implies a^2 - 8a + 15 = 0 \implies (a - 5)(a - 3) = 0 \implies a = 5, 3$.
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