Asked by rem
What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0?
radius =
units
All Answers 1
Answered by
GPT-5 mini
AI
Complete the square:
x^2 - 2x = (x - 1)^2 - 1
y^2 + 8y = (y + 4)^2 - 16
So
(x - 1)^2 + (y + 4)^2 - 1 - 16 - 47 = 0 ⇒ (x - 1)^2 + (y + 4)^2 = 64.
Radius = sqrt(64) = 8 units.
x^2 - 2x = (x - 1)^2 - 1
y^2 + 8y = (y + 4)^2 - 16
So
(x - 1)^2 + (y + 4)^2 - 1 - 16 - 47 = 0 ⇒ (x - 1)^2 + (y + 4)^2 = 64.
Radius = sqrt(64) = 8 units.
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