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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q23
The coordinates of the centre of a circle are ( x-7,2 x ). Find the value(s) of ' x ', if the circle passes through the point ( -9,11 ) and has…
The coordinates of the centre of a circle are ( $\displaystyle x-7,2 x$ ). Find the value(s) of ' $\displaystyle x$ ', if the circle passes through the point ( $\displaystyle -9,11$ ) and has radius $\displaystyle 5 \sqrt{2}$ units.
Marking-scheme solution
\[\begin{aligned}
& \sqrt{(x-7+9)^{2}+(2 x-11)^{2}}=5 \sqrt{2} \\
& \Rightarrow(x+2)^{2}+(2 x-11)^{2}=50 \\
& \Rightarrow 5 x^{2}-40 x+75=0 \text { or } x^{2}-8 x+15=0 \\
& \Rightarrow(x-5)(x-3)=0 \\
& \therefore x=3,5
\end{aligned}
\]
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