Q104 / 180 · KCET 2013 · Mathematics

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
Correct answer
D
6

Solution

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 $\begin{aligned} &=2 \sqrt{f^{2}-c} \\ &=2 \sqrt{(1)^{2}-(-8)} \\ &=2 \sqrt{1+8}=2 \sqrt{9} \\ &=2 \times 3=6 \end{aligned}$

Hence, the correct answer is option: 'D'.

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