Answered

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transform the standard form of the equation of a circle into general form (x-3)²+(y+4)²=16​

Sagot :

KAntoineDoixidn

✒️CIRCLE EQUATION

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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]

  • what solution of general form of (x-3)² + (y+4)² = 16

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \large\: \rm{x^2 + y^2 - 6x + 8y + 9 = 0} [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

» The general form of the equation of the circle is written as:

  • [tex] x^2 + y^2 + Ax + By + C = 0 [/tex]

» Rearrange the given equation.

  • [tex] (x-3)^2 + (y+4)^2 = 25 [/tex]

  • [tex] \small x^2 - 6x + 9 + y^2 + 8y + 16 = 16 [/tex]

  • [tex] \small x^2 + y^2 - 6x + 8y + 9 + 16 - 16 = 0 [/tex]

  • [tex] \small x^2 + y^2 - 6x + 8y + 9 = 0 [/tex]

[tex] \therefore [/tex] x² + y² - 6x + 8y + 9 = 0 is the general form of the given equation of the circle.

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