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  •  Equation <img alt="\mathrm{a x^{2}+2 h x y+b y^{2}=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Ba%20x%5E%7B2%7D&plus;2%20h%20x%20y&plus;b%20y%5E%7B2%7D%3D0%7D"

 Equation \mathrm{a x^{2}+2 h x y+b y^{2}=0}  represents a pairs of lines, combined equation of lines that can be obtained by taking the mirror of lines about the \mathrm{x}-axis is

Option: 1

\mathrm{a x^{2}+2 h x y+b y^{2}=0}


Option: 2

\mathrm{b x^{2}+2 h x y+a y^{2}=0}


Option: 3

\mathrm{b x^{2}-2 h x y+a y^{2}=0}


Option: 4

none of these


Answers (1)

best_answer

Let the lines represented by \mathrm{a x^{2}+b y^{2}+2 h x y=0\, be \, y=m_{1} x\, and \, y=m_{2} x,then \: m_{1}+m_{2}=\frac{-2 \mathrm{~h}}{\mathrm{~b}}}, \mathrm{m_{1} m_{2}=a / b}. If these lines reflected about the x-axis, there equation becomes \mathrm{y+m_{1} x= 0\, and \, y+m_{2} x=0} and their combined equation is \mathrm{\left(y+m_{1} x\right)\left(y+m_{2} x\right)=0}

\mathrm{\Rightarrow y^{2}+x y\left(m_{1}+m_{2}\right)+m_{1} m_{2} x^{2}=0}
\mathrm{\Rightarrow \mathrm{by}^{2}-2 \mathrm{hxy}+a \mathrm{x}^{2}=0}

 

Posted by

HARSH KANKARIA

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