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The coordinates of the centre of a circle are $(x-7, 2x)$. Find the value(s) of '$x$', if the circle passes through the point $(-9, 11)$ and has radius $5\sqrt{2}$ units.
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$(x - 7 + 9)^2 + (2x - 11)^2 = (5\sqrt{2})^2$ (1/2 Mark)
$(x + 2)^2 + (2x - 11)^2 = 50$ (1/2 Mark)
$\implies 5x^2 - 40x + 75 = 0$ or $x^2 - 8x + 15 = 0$ (1/2 Mark)
$\implies (x - 5)(x - 3) = 0$ (1/2 Mark)
$\therefore x = 3,5$ (1/2 + 1/2 Mark)
$(x + 2)^2 + (2x - 11)^2 = 50$ (1/2 Mark)
$\implies 5x^2 - 40x + 75 = 0$ or $x^2 - 8x + 15 = 0$ (1/2 Mark)
$\implies (x - 5)(x - 3) = 0$ (1/2 Mark)
$\therefore x = 3,5$ (1/2 + 1/2 Mark)