Points A (–1, y) and B (5, 7) lie on a circle with centre C (2, –3y). Find the radius of the circle.
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we know, if A and B lies on circle and C is the centre of circle , then line joining of points A and B is intersected by Centre of circle.
e.g., O lies on midpoint of AB. means, we have to use midpoint section formula.
here, A (-1, y) and B(5,7) lies on circle with centre C(2,-3y) .
A--------------C------------------B
now, use midpoint section formula,
[if (x,y) is the midpoint of (x1,y1) and (x2, y2) then, x = (x1 + x2)/2 and y = (y1+y2)/2 ]
so, -3y = (y + 7)/2
=>-6y = y + 7
=> -7y = 7
=> y = -1
now, centre of circle = (2, 3)
so, radius = length of CB = √{(2-5)² + (3 - 7)²}
radius of circle = √{9 + 16} = 5 unit
e.g., O lies on midpoint of AB. means, we have to use midpoint section formula.
here, A (-1, y) and B(5,7) lies on circle with centre C(2,-3y) .
A--------------C------------------B
now, use midpoint section formula,
[if (x,y) is the midpoint of (x1,y1) and (x2, y2) then, x = (x1 + x2)/2 and y = (y1+y2)/2 ]
so, -3y = (y + 7)/2
=>-6y = y + 7
=> -7y = 7
=> y = -1
now, centre of circle = (2, 3)
so, radius = length of CB = √{(2-5)² + (3 - 7)²}
radius of circle = √{9 + 16} = 5 unit
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