Johnston Turnbull
01/17/2024 · Junior High School
Write the standard form of the equation of the circle described below. Center \( (3,-4), \mathrm{r}=4 \) The standard form of the equation of the circle is (Type andion. Simplify your answer.)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((3, -4)\) and the radius \(r\) is \(4\).
Substituting \(h = 3\), \(k = -4\), and \(r = 4\) into the equation, we get:
\[
(x - 3)^2 + (y + 4)^2 = 4^2
\]
Calculating \(4^2\):
\[
4^2 = 16
\]
Thus, the equation becomes:
\[
(x - 3)^2 + (y + 4)^2 = 16
\]
So, the standard form of the equation of the circle is:
\[
\boxed{(x - 3)^2 + (y + 4)^2 = 16}
\]
Quick Answer
\((x - 3)^2 + (y + 4)^2 = 16\)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit