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mathgeometrywolfram-mathematica
Androvich
Androvich

Reputation: 1130

Mathematica Rewriting Circle Equation

I have a circle with the expression:

x^2+y^2+10x-14y-7=0

I need to find the radius and the coordinates to the center of the circle using Wolfram Mathematica; in Symbolab it tells me to rewrite the expression in the form of the standard eclipse equation.

I know that the answer should be c=(x+5)^2 + (y-7)^2 = 81, so the radius is sqrt(81) = 9 ...

How is this achievable in Mathematica (I'm very new to this...)?

Thanks and best regards (-:

Upvotes: 0

Views: 317

Answers (2)

agentp
agentp

Reputation: 6989

Solve[{
 CoefficientList[x^2 + y^2 + 10 x - 14 y - 7, {x, y}]
  ==
  CoefficientList[(x - xc)^2 + (y - yc)^2 -  r^2, {x, y} ],r>0}
 , {xc, yc, r}]

{{xc -> -5, yc -> 7, r -> 9}}

Upvotes: 0

Szabolcs
Szabolcs

Reputation: 25703

For example,

SolveAlways[{x^2 + y^2 + 10 x - 14 y - 7 == (x - a)^2 + (y - b)^2 - r^2}, {x, y}]

Upvotes: 2

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