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find the equation of the circle which has its centre on the line y=2 and which passes through the points (2,0)and(4,0)

find the equation of the circle which has its centre on the line y=2 and which passes through the points (2,0)and(4,0)

Grade:Select Grade

1 Answers

Vikas TU
14149 Points
4 years ago
equation of the circle which passes through (2,0) is given by
  • (2-h)^2 + ( 0 – k )^2 = r^2
  • 4 + h^2 -4h + k^2 = r^2------------------------1
equation of the circle which passes through (4,0) is given by
 
  • (4-h)^2 + ( 0 – k )^2 = r^2
  • 16 + h^2 – 8h +k^2 = r^2--------------------2
4 + h^2 -4h + k^2 = 16 + h^2 – 8h +k^2
 
4 - 4h = 16 – 8h
4h = 12
h= 3.
 
Since center on the line y=2
k=2.
 
Hence the center of circle is (3,2)
From equation 1
4 + 3^2 -4(3) + 2^2 = r^2
r^2 = 4 + 9 – 12 + 4
r^2 = 5
r = (5) ^ ½
 
Equation of circle is
 
  • (x-3)^2 + ( y – 2 )^2 = 5.

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