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Question

The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

A
x2+y2+2x+3y5=0
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B
6(x2+y2)5(3x+2y)=0
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C
x2+y22x3y+5=0
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D
6(x2+y2)+5(3x+2y)=0
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Solution

The correct option is B 6(x2+y2)5(3x+2y)=0
Given, triangle formed by the lines x = 0, y = 0, 2x + 3y = 5, so vertices of the triangle are (0, 0), (5/2, 0) and (0, 5/3).

Since circle is passing through (0, 0).

Equation of circle will be x2+y2+2gx+2fy=0 ...(i)

Also, circle is passing through (5/2, 0) and (0, 5/3)
So, g = -5/4, f = -5/6.
Put the values of g and f in equation (i).
After solving, we get 6(x2+y2)5(3x+2y)=0, which is the required equation of the circle.


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