Answer:
The equation of the circle is (x + 5)² + (y + 12)² = 13²
OR
The equation of the circle is (x + 5)² + (y + 12)² = 169
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation of the circle of center (h , k) and radius r is:
(x - h)² + (y - k)² = r²
- The length of the radius is the distance between the center (h , k)
and any point on the circle (x1 , y1)
- [tex]r=\sqrt{(h-x_{1})^{2}+(k-y_{1})^{2}}[/tex]
* Lets solve the problem
∵ The center of the circle is (-5 , -12)
∴ h = -5 and k = -12
∵ The circle passes through the origin
∴ The origin (0 , 0) lies on the circle
∴ x1 = 0 , y1 = 0
∵ [tex]r^{2}=(h-x_{1})^{2}+(k-y_{1})^{2}[/tex]
∴ r² = (-5 - 0)² + (-12 - 0)² = (-5)² + (-12)² = 25 + 144 = 169
∴ r = √169 = 13 units
* Lets write the equation of the circle
∵ h = -5 , k = -12 , r² = 169 or 13²
∵ The equation of the circle is (x - h)² + (y - k)² = r²
∴ The equation of the circle is (x - -5)² + (y - -12)² = 13²
∴ The equation of the circle is (x + 5)² + (y + 12)² = 13²
