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Question
A circle has radius 3 units and its centre lies on the line y = x - 1. If it passes through the point (7, 3), find its equations.
A circle has radius 3 units and its centre lies on the line y = x - 1. If it passes through the point (7, 3), find its equations.
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Solution
Given circle has radius= 3
By distance formula,
(a−7)2+(b−3)2=9 …(1)
(a, b) lies on y = x - 1
b = a - 1
Substituiing b in (1), we get
(a−7)2+(a−4)2=9a2−14a+49+a2−8a+16=92a2−22a+56=0a2−11a+28=0(a−7)(a−4)=0(a−7),(a−4)=0b=6,b=3
Equations of circle are,
(x−7)2+(y−6)2=9x2−14x+49+y2−12y+36=9x2−14x−12y+y2+76=0(x−4)2+(y−3)2=9x2−8x+16+y2−6y+9=9x2+y2−8x−6y+16=0
Given circle has radius= 3
By distance formula,
(a−7)2+(b−3)2=9 …(1)
(a, b) lies on y = x - 1
b = a - 1
Substituiing b in (1), we get
(a−7)2+(a−4)2=9a2−14a+49+a2−8a+16=92a2−22a+56=0a2−11a+28=0(a−7)(a−4)=0(a−7),(a−4)=0b=6,b=3
Equations of circle are,
(x−7)2+(y−6)2=9x2−14x+49+y2−12y+36=9x2−14x−12y+y2+76=0(x−4)2+(y−3)2=9x2−8x+16+y2−6y+9=9x2+y2−8x−6y+16=0
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