KCET · Maths · Circle
The length of the chord of the circle \(x^{2}+y^{2}+3 x+2 y-8=0\) intercepted by the \(y\)-axis is
- A 3
- B 8
- C 9
- D 6
Answer & Solution
Correct Answer
(D) 6
Step-by-step Solution
Detailed explanation
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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