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Question

A triangle is formed by the lines whose combined equation is given by x+y-4xy-x-y+2=0 The equation of its circumcircle is


A

x2+y25x3y+8=0

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B

x2+y23x5y+8=0

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C

x2+y23x5y-8=0

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D

none of these

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Solution

The correct option is B

x2+y23x5y+8=0


Explanation for correct option:

Step-1: Simplify the given data.

Given, x+y-4xy-x-y+2=0

x+y-4x-1y-2=0

Therefore, the sides of triangle are x+y-4=0,x-1=0&y-2=0.

Step-2: Draw the triangle using given sides.

We know that In a right angle triangle circumcentre is on mid-point of hypotenuse.

Therefore, circumcentre is 1+22,3+22.

Circumradius is 122-12+2-32=12

Step-3: Equation of circumcircle.

we know that equation of circle having center x1,y1 and radius r1 is x-x12+y-y12=r12

Therefore equation of circumcircle is x-322+y-522=122

x2+94-3x+y2+254-5y=12

4x2-12x+4y2-20y+34-24=0

4x2+y2-3x-5y+8=0

x2+y2-3x-5y+8=0

Hence correct answer is option B


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