The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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