Answer to Question #290149 in Analytic Geometry for Love

Question #290149

What are the center radius form of a circle defined by x²+y²–2x+4y–1=0

1
Expert's answer
2022-01-24T18:29:49-0500
x2+y22x+4y1=0x^2+y^2-2x+4y-1=0

(x22x+1)+(y2+4y+4)=6(x^2-2x+1)+(y^2+4y+4)=6

(x1)2+(y+2)2=(6)2(x-1)^2+(y+2)^2=(\sqrt{6})^2

The center-radius form of the circle equation is

(x1)2+(y+2)2=(6)2,(x-1)^2+(y+2)^2=(\sqrt{6})^2,

with the center at (1,2)(1, -2) and the radius 6.\sqrt{6}.


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