The diameter of a circle are along 2x+y-7=0 and X+3y-11=0 then the equation of this circle, which also passes through (5,7) is

Answers (1)

Diameyter of the circle :

2x+y-7=0 ....(i)

x+3y-11=0....(ii)

Diameter intesect at the centre of the circle

Equation (i) - 2xEquation (ii)

2x + y -7 -2x - 6y +22 =0

5y = 15

y =3

x = 11 - 3(3) = 2

Centre of the circle (2,3)

Equation of the circle 

(x-2)2 + (y-3)2 = r2 

Circle passes through point (5,7) 

So (5-2)2 + (7-3)2 = r2 

(3)2 + (4)2 = r2 

r2 = 25

Equation of the circle :  (x-2)2 + (y-3)2 = 25 

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