Question

Find the equation of the circum circle of the triangle formed by the coordinate axes and the straight line 2x + 3y = 6

Answer 1

Equation of line ⇒ 2x + 3y = 6
divide by 6 on both side
x/3 + y/2 = 1
co-ordinate of the x intersept = (3, 0)
co-ordinate of the y intersept = (0, 2)
so co-ordinate of the triangel formed by line = (0, 0), (3, 0), (0, 2)
let the equation of circum circle is  $x^{2}$ + $y^{2}$ - 2gx - 2fy + h = 0
as circum circle passes through all three point so all three point must satisfy the equation of circle.
putting (0, 0)
0 + 0 - 0 - 0 + h = 0
h = 0
putting (3, 0)
$3^{2}$ + 0 - 2×3×g -2×0×f = 0
g = 3/2
putting (0, 2)
0 + $2^{2}$ - 2×0×g - 2×2f = 0
f = 1
now putting f, g, h value in equation of circum circle
we get
$x^{2}$ + $y^{2}$ - 3x - 2y = 0