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Determine the centre and radius of the circle with the equation x2+y2−6x+10y−15=0.

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5.1 Determine the centre and radius of the circle with the equation x2+y2−6x+10y−15=0x^2+y^2-6x+10y-15=0.

  1. Group the x-terms and y-terms, and move the constant to the right side of the equation.

    x2−6x+y2+10y=15x^2 - 6x + y^2 + 10y = 15

  2. Complete the square for the x-terms and y-terms.

    For x2−6xx^2 - 6x, add (−62)2=(−3)2=9(\frac{-6}{2})^2 = (-3)^2 = 9.
    For y2+10yy^2 + 10y, add $(\frac{10

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