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the equation of a diameter of a circle is 2x-y+4=0 and it passes through the points (4,6)and(1,9).Find te equations of the circle,the coordinates of its centre and length of its radius

Profile image of aradhya singh
9 Years agoGrade Select Grade
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1 Answer

Profile image of Vikas TU
9 Years ago
Since center of circle lies on diameter => 2h-k+4=0
Since circle lies on (4,6)and(1,9)
(4-h)^2 + (6-k)^2 = (1-h)^2 + (9-k)^2
=> -8h -12k +16+36 = -2h -18k +1+81
=> -6h +6k = 30
=>h=5
Substituting h=5 in diameter line we get k=10
For finding radius
(4-h)^2 + (6-k)^2 = r^2
Substituting values of h and k
=> r= (17)^1/2
Equation of circle is
(x-5)^2 +(k-10)^2 = 17

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