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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 1 · Set 1 · Q23
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…
The coordinates of the centre of a circle are (2a, a - $\displaystyle 7$). Find the value(s) of 'a' if the circle passes through the point $\displaystyle (11, -9)$ and has diameter $\displaystyle 10 \sqrt{2}$ units.
Marking-scheme solution
\[\begin{aligned}
& \text { radius }=5 \sqrt{2} \text { units } \\
& \quad(2 \mathrm{a}-11)^{2}+(\mathrm{a}-7+9)^{2}=50 \\
& \Rightarrow \mathrm{a}^{2}-8 \mathrm{a}+15=0 \\
& \Rightarrow(\mathrm{a}-5)(\mathrm{a}-3)=0 \\
& \Rightarrow \mathrm{a}=5,3
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.