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  • The length of the common chord of the circles <img alt="\mathrm{x^{2}+y^{2}+2 x+3 y+1=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E%7B2%7D&plus;y%5E%7B2%7D&plus;

The length of the common chord of the circles \mathrm{x^{2}+y^{2}+2 x+3 y+1=0} and \mathrm{x^{2}+y^{2}+4 x+3 y+2=0}, is

Option: 1

\frac{9}{2}


Option: 2

2 \sqrt{2}


Option: 3

3 \sqrt{2}


Option: 4

\frac{3}{2}


Answers (1)

best_answer

Equation of common chord is \mathrm{2 x+1=0 \Rightarrow x=-1 / 2}
This cuts the circle at points  \mathrm{\left(-\frac{1}{2}\right)^{2}+y^{2}+2\left(-\frac{1}{2}\right)+3 y+1=0}

\mathrm{\Rightarrow \frac{1}{4}+y^{2}-1+3 y+1=0}
\mathrm{\Rightarrow 4 \mathrm{y}^{2}+12 \mathrm{y}+1=0}
\mathrm{\Rightarrow \mathrm{y}=\frac{-12 \pm 8 \sqrt{2}}{8}=\frac{-3 \pm 2 \sqrt{2}}{2}}
\mathrm{\therefore length =2 \sqrt{2}}.

Hence (B) is the correct answer.

 

Posted by

SANGALDEEP SINGH

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