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Determine the center and radius of the following circle equation:
x^2+y^2-6x-8y+24=0

User GgPeti
by
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1 Answer

3 votes

Center is (3, -4) and radius is 1

Explanation:

  • Step 1: Find center and radius of the circle with equation x² + y² - 6x - 8y + 24 = 0

The standard form of the equation of a circle is x² + y² + 2gx +2fy + c = 0, where center is (-g, -f) and radius = √g² + f² - c

By comparing the 2 equations, 2g = -6, 2f = 8 and c = 24

⇒ g = -6/2 = -3

⇒ f = 8/2 = 4

c = 24

  • Step 2: Find center.

Center = (-g. -f) = (3, -4)

  • Step 3: Find radius.

Radius = √g² + f² - c = √3² + (-4)² - 24

= √9 + 16 - 24 = √1 = 1

User Ido Green
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