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  • Let PQR be a right angled isosceles triangle, right angled at P(2,1). If the equation of the line QR is <img alt="\mathrm{2 x+y=3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B

Let PQR be a right angled isosceles triangle, right angled at P(2,1). If the equation of the line QR is \mathrm{2 x+y=3}, then the equation representing the pair of lines PQ and PR is

Option: 1

\mathrm{3 x^{2}-3 y^{2}+8 x y+20 x+10 y+25=0}


Option: 2

\mathrm{3 x^{2}-3 y^{2}+8 x y-20 x-10 y+25=0}


Option: 3

\mathrm{3 x^{2}-3 y^{2}+8 x y+10 x+15 y+20=0}


Option: 4

\mathrm{3 x^{2}-3 y^{2}-8 x y-10 x-15 y-20=0}


Answers (1)

best_answer

The line PQ and PR will be inclined at an angle of 45^{\circ} with the line \mathrm{2 x+y=3}

\mathrm{\Rightarrow 1=\left|\frac{m+2}{1-2 m}\right|}
\mathrm{\Rightarrow m=-\frac{1}{3}, 3}
Hence the lines are \mathrm{y-1=-\frac{1}{3}(x-4) \: and \: y-1=3(x-2)}

Find the equation of pair of lines by multiplying these two equations.

Hence (B) is the correct answer.


 

Posted by

jitender.kumar

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