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  • Let PQR be the 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

Let PQR be the 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

b

If \mathrm{m} is the slope of slide PQ and PR, then

\mathrm{\frac{m-(-2)}{1+(-2) m}= \pm \tan \pi / 4}, \mathrm{\square} slope of QR is -2 and \mathrm{\angle \mathrm{PQR}=\angle \mathrm{PRQ}=45^{\circ}}

\mathrm{\Rightarrow m=3,-1 / 3}

\mathrm{\therefore }  Equations of side PQ and PR are 

\mathrm{3 x-y-5=0 \text { and } x+3 y-5=0}  

Their combined equation is 

\mathrm{\begin{aligned} & (3 x-y-5)(x+3 y-5)=0 \\\\ & \text { i.e. } 3 x^2-3 y^2+8 x y-20 x-10 y+25=0 \end{aligned}}

Which is given in (b).

Posted by

chirag

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