The equation x^2+y2-4x+2y=b describe a circle

Answers

Answer 1

Answer: $x^2+y^2-4x+2y=b\implies~x^2-4x+4+y^2+2y+1=b+5\implies~(x-2)^2+(y+1)^2=b+5$

This describes a circle centered at $(2,-1)$ with radius $√(b+5)$ .

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Quadratic graph find a and b

Answers

Answers: a = -9 and b = -2

Reason

The template $y = (x+a)^2 + b$ is very close to the vertex form $y = c(x-h)^2+k$ where the vertex is (h,k). The vertex represents either the highest point or the lowest point on the parabola (depending if the parabola opens downward or upward).