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The length of the chord of the circle $x^{2}+y^{2}+3 x+2 y-8=0$ intercepted by the $y$-axis is
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2666 Upvotes
Verified Answer
The correct answer is:
6
Given equation of circle is
$x^{2}+y^{2}+3 x+2 y-8=0$
On comparing with
$\begin{array}{r}
x^{2}+y^{2}+2 g x+2 f y+c=0, \text { we get } \\
g=\frac{3}{2}, \quad f=1 \text { and } c=-8
\end{array}$
Now, intercept made by $y$-axis
$\begin{aligned}
&=2 \sqrt{f^{2}-c} \\
&=2 \sqrt{(1)^{2}-(-8)} \\
&=2 \sqrt{1+8}=2 \sqrt{9} \\
&=2 \times 3=6
\end{aligned}$
$x^{2}+y^{2}+3 x+2 y-8=0$
On comparing with
$\begin{array}{r}
x^{2}+y^{2}+2 g x+2 f y+c=0, \text { we get } \\
g=\frac{3}{2}, \quad f=1 \text { and } c=-8
\end{array}$
Now, intercept made by $y$-axis
$\begin{aligned}
&=2 \sqrt{f^{2}-c} \\
&=2 \sqrt{(1)^{2}-(-8)} \\
&=2 \sqrt{1+8}=2 \sqrt{9} \\
&=2 \times 3=6
\end{aligned}$
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