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If the line $3 x-2 y+6=0$ meets $X$-axis and $Y$-axis, respectively at $A$ and $B$, then the equation of the circle with radius $A B$ and centre at $A$ is
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Verified Answer
The correct answer is:
$x^2+y^2+4 x-9=0$
Since, the line $3 x-2 y+6=0$ meets the coordinates axes, therefore
$\therefore$ Points are $A(-2,0)$ and $B(0,3)$.
$$
\because \text { Radius }=A B=\sqrt{2^2+3^2}=\sqrt{13}
$$
$\therefore$ The equation of circle, whose centre $(-2,0)$ and radius $\sqrt{13}$, is
$$
\begin{aligned}
& (x+2)^2+(y-0)^2=(\sqrt{13})^2 \\
& \Rightarrow \quad x^2+y^2+4 x+4=13 \\
& \Rightarrow \quad x^2+y^2+4 x-9=0 \\
&
\end{aligned}
$$
$\therefore$ Points are $A(-2,0)$ and $B(0,3)$.
$$
\because \text { Radius }=A B=\sqrt{2^2+3^2}=\sqrt{13}
$$
$\therefore$ The equation of circle, whose centre $(-2,0)$ and radius $\sqrt{13}$, is
$$
\begin{aligned}
& (x+2)^2+(y-0)^2=(\sqrt{13})^2 \\
& \Rightarrow \quad x^2+y^2+4 x+4=13 \\
& \Rightarrow \quad x^2+y^2+4 x-9=0 \\
&
\end{aligned}
$$
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