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Circle — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsCircle2 Marks
Question
Find the equation of a circle whose centre is $(-3,1)$ and which pass through the point $(5,2)$.
✓

Answer

Centre $\mathrm{C}=(-3,1)$,
Circle passes through the point $\mathrm{P}(5,2)$.
By distance formula,
$
\begin{aligned}
r^2=\mathrm{CP}^2 & =(5+3)^2+(2-1)^2 \\
& =8^2+1^2=64+1=65
\end{aligned}
$
$\therefore$ the equation of the circle is
$
\begin{aligned}
& (x+3)^2+(y-1)^2=65 \quad \text { (centre-radius form) } \\
& x^2+6 x+9+y^2-2 y+1=65 \\
& x^2+y^2+6 x-2 y+10-65=0 \\
& x^2+y^2+6 x-2 y-55=0
\end{aligned}
$

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