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Question

If the equations of two diameters of a circle arc 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.

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Solution

The equation of two diameter of the circle
(xa)2+(yb)2=r2 (A)is2x+y=6 (i)3x+2y=4 (ii)
By solving (i) and (ii) we will get
x=8,y=10
4x+2y=123x+2y=4 ––––––––––x = +8––––––––––
Also 2(8)+y=616+y=6y=616y=10
The point of intersection of (l) and (2) is C (8, -10), which is the centre of circle. Also, radius = 10
From (A)
(x8)2+(y+10)2=102x2+y216x+20y+64=0


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