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(x-3)^2+(y+5)^2=36

2 min read Jun 17, 2024
(x-3)^2+(y+5)^2=36

The Circle Defined by (x-3)^2 + (y+5)^2 = 36

The equation (x-3)^2 + (y+5)^2 = 36 represents a circle in the standard form of the circle equation:

(x - h)^2 + (y - k)^2 = r^2

where:

  • (h, k) represents the center of the circle
  • r represents the radius of the circle

Let's analyze the equation (x-3)^2 + (y+5)^2 = 36:

Center of the Circle

  • Comparing our equation with the standard form, we can see that h = 3 and k = -5.
  • Therefore, the center of the circle is (3, -5).

Radius of the Circle

  • We have r^2 = 36.
  • Taking the square root of both sides gives us r = 6.
  • The radius of the circle is 6 units.

Summary

The equation (x-3)^2 + (y+5)^2 = 36 defines a circle with:

  • Center: (3, -5)
  • Radius: 6 units

This circle is centered at the point (3, -5) and has a radius of 6 units.

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