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\mathrm{ABC} is a right angled isosceles triangle, right angled at \mathrm{\mathrm{A}(2,1)}. If the equation of side \mathrm{\mathrm{BC} \: \: is \: \: 2 x+y=3}, then the combined equation of lines \mathrm{\mathrm{AB} \: and \: \mathrm{AC}} is -
 

Option: 1

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


 


Option: 2

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

 


Option: 3

3 \mathrm{x}_2-3 \mathrm{y} 2+8 \mathrm{xy}+10 \mathrm{x}+15 \mathrm{y}+20=0


Option: 4

\text{ None of these}


Answers (1)

best_answer

We have \angle \mathrm{B}=\angle \mathrm{C}=. Let ' \mathrm{m} ' be the slope of side \mathrm{AB} then \mathrm{1=\left|\frac{m-2}{1+2 m}\right|.}

\mathrm{\Rightarrow \mathrm{m}=\frac{1}{3}, \mathrm{~m}=-3}

Thus equation of equal sides are \mathrm{x - 3y + 1 = 0\: and\: 3x + y - 7 = 0.}

Their combined equation is \mathrm{(x - 3y + 1)(3x + y - 7) = 0}  i.e.,

\mathrm{3x2 -3y2 -8xy - 4x + 22y -7 = 0}

Hence option 4 is correct.

Posted by

Rakesh

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