Write the standard form of the equation of the circle with the given characteristics.
Center: ; Radius:

Ask by Ellis Wang. in the United States

Jan 27,2025

Question

Write the standard form of the equation of the circle with the given characteristics. Center: $$ (2,-9) $$; Radius: $$ \sqrt{19} $$ $$ \square $$

UpStudy AI · Accepted Answer

The standard form of the equation of a circle is:

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

where $$(h, k)$$ is the center of the circle and $$r$$ is the radius.

Given:
- Center $$(h, k) = (2, -9)$$
- Radius $$r = \sqrt{19}$$

Substituting these values into the standard form:

$$
(x - 2)^2 + (y + 9)^2 = (\sqrt{19})^2
$$

Simplifying the equation:

$$
(x - 2)^2 + (y + 9)^2 = 19
$$

**Final Answer:**
$$
(x - 2)^2 + (y + 9)^2 = 19
$$
The standard form of the circle's equation is $$(x - 2)^2 + (y + 9)^2 = 19$$.

Write the standard form of the equation of the circle with the given characteristics.
Center: ; Radius: