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  • The image of the pair of lines represented by <img alt="\mathrm{a x^2+2 h x y+b y^2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Ba%20x%5E2&plus;2%20h%20x%20y&plus;b%

The image of the pair of lines represented by \mathrm{a x^2+2 h x y+b y^2=0} by the line mirror \mathrm{y=0} is
 

Option: 1

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



 


Option: 2

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

The line mirror \mathrm{y=0, makes\: P(x, y) \rightarrow Q(x,-y) }

Replacing \mathrm{\: y \: by -y } in the given pair of equations

\mathrm{a x^2+2 h x y+b y^2=0}, we get the required pair of lines as \mathrm{a x^2+2 h x(-y)+b(-y)^2=0}
Or \mathrm{a x^2-2 h x y+b y^2=0}.

Hence option 2 is correct.

Posted by

Pankaj Sanodiya

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