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Class 10 › Mathematics › Coordinate Geometry
CBSE2026Class Class 10 · Mathematics2 Marks · Short✅ Verified
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.
✅ Answer & Solution
Distance from centre to a point on the circle = radius. $\sqrt{(x-7-(-9))^2+(2x-11)^2} = 5\sqrt{2}$. $(x+2)^2+(2x-11)^2 = 50$. $x^2+4x+4+4x^2-44x+121=50$. $5x^2-40x+125=50$. $5x^2-40x+75=0$. $x^2-8x+15=0$. $(x-3)(x-5)=0$. $x=3$ or $x=5$.
