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  • A triangle is formed by the lines whose combined equation is given by : <img alt="\mathrm{(x+y-4)}\: \mathrm{(x y-3 x-2 y+6)}=0" src="https://entrancecorner.onc

A triangle is formed by the lines whose combined equation is given by :

\mathrm{(x+y-4)}\: \mathrm{(x y-3 x-2 y+6)}=0.The equation of its circumcircle is 

 

 

Option: 1

\mathrm{x^2+y^2-5 x-3 y+8=0}


Option: 2

\mathrm{x^2+y^2-3 x-5 y+8=0}


Option: 3

\mathrm{x^2+y^2-3 x-5 y-8=0}


Option: 4

none of these


Answers (1)

best_answer

The sides are \mathrm{x + y - 4 = 0, x - 2 = 0, y - 3 = 0}

So, the triangle is right angled at (2, 3). 

The hypotenuse is \mathrm{x + y - 4 = 0} whose ends are (1, 3) and (2, 2).

The circumcentre =\left(\frac{1+2}{2}, \frac{3+2}{2}\right) and

circumradius  

                       =\frac{1}{2} \sqrt{(1-2)^2+(3-2)^2}=\frac{1}{\sqrt{2}}

Posted by

vishal kumar

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