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If slope of one line of \(a x^2+4 x y+y^2=0\) is 3 times the other, then the value of ' \(a\) ' is
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The correct answer is:
3
Let the slope of lines are \(m\) and \(3 m\) respectively which are represented by \(a x^2+4 x y+y^2=0\)
\(\because\) Sum of slopes \(=m+3 m=-\frac{4}{1}=-4 \Rightarrow m=-1\) and product of the slopes \(=m(3 m)=\frac{a}{1} \Rightarrow m^2=\frac{a}{3}\)
\(\therefore \quad(-1)^2=\frac{a}{3} \Rightarrow a=3\)
Hence, option (c) is correct.
\(\because\) Sum of slopes \(=m+3 m=-\frac{4}{1}=-4 \Rightarrow m=-1\) and product of the slopes \(=m(3 m)=\frac{a}{1} \Rightarrow m^2=\frac{a}{3}\)
\(\therefore \quad(-1)^2=\frac{a}{3} \Rightarrow a=3\)
Hence, option (c) is correct.
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