The equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289
Equation of a circle
The standard equation of a circle is expressed as shown
(x-a)^2 + (y-b)^2 = r^2
where:
(a, b) is the centre
r is the radius
Given the following
Centre = (-7, -1)
Determine the radius
r = √(8+7)² +(7+1)²
r² = 15² + 8²
r² = 225 + 64
r² = 289
Substitute the centre and radius
(x-(-7))^2 + (y-(-1))^2 = 289
(x+7)² +(y+1)² = 289
Hence the equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289
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