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Katarinachaenggo
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The standard equation of a circle with the center at (h, k) and a radius of r units is (x – h)²+ (y – k)² = r². Given the cross section which is a circle, find the equation of a circle in standard form with center at (0, -5) and one point on the circle is (2, 3).
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KizunaHighgo

EQUATION OF THE CIRCLE

Given

  • Point of the center = (0,-5)
  • One point of the circle = (2,3)

Find the distance between the two points.

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(2 - 0)² + (3 - (-5))²

d = √(2)² + (8)²

d = √4 + 64

d = √68

d = 2√17

The distance will be the radius of the circle.

Use the equation (x – h)²+ (y – k)² = r² to find the standard equation of the circle

(x – h)²+ (y – k)² = r²

x² + (y + 5)² = (2√17)²

x² + (y + 5)² = (4)(17)

x² + (y + 5)² = 68

[tex] \: [/tex]

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