MHT CET · Maths · Circle
The area of the circle centred at \((1,2)\) and passing through \((4,6)\), is
- A \(5 \pi\) sq unit
- B \(10 \pi\) sq unit
- C \(25 \pi\) sq unit
- D None of these
Answer & Solution
Correct Answer
(C) \(25 \pi\) sq unit
Step-by-step Solution
Detailed explanation
The equation of a circle centred at \((1,2)\) and passing through \((4,6)\) is
\(
\begin{array}{l}
(x-1)^{2}+(y-2)^{2}=(4-1)^{2}+(6-2)^{2} \\
\Rightarrow x^{2}+y^{2}-2 x-4 y+1+4=9+16 \\
\Rightarrow \quad x^{2}+y^{2}-2 x-4 y-20=0
\end{array}
\)
Now, radius
\(
=\sqrt{(-1)^{2}+(-2)^{2}+20}
\)
\(
=\sqrt{1+4+20}=5
\)
\(\therefore \quad\) Area of circle \(=\pi r^{2}\)
\(=25 \pi\) sq unit
\(
\begin{array}{l}
(x-1)^{2}+(y-2)^{2}=(4-1)^{2}+(6-2)^{2} \\
\Rightarrow x^{2}+y^{2}-2 x-4 y+1+4=9+16 \\
\Rightarrow \quad x^{2}+y^{2}-2 x-4 y-20=0
\end{array}
\)
Now, radius
\(
=\sqrt{(-1)^{2}+(-2)^{2}+20}
\)
\(
=\sqrt{1+4+20}=5
\)
\(\therefore \quad\) Area of circle \(=\pi r^{2}\)
\(=25 \pi\) sq unit
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