https://file.aiquickdraw.com/mathbot/file/172666953589709mkg6y9.jpg

I Found Point B And M

M Is (29,0)
and B is (4,0)
I need to find the Equation of a circle
and Point C

To find the equation of the circle and the coordinates of point \( C \), we can follow these steps:

### 1. **Equation of the Circle**:
We know:
- The radius \( r \) of the circle is given as 20.
- The center of the circle, \( M \), is at \( (29, 0) \).

The general form of the equation of a circle is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \( (h, k) \) is the center and \( r \) is the radius.

Using the given information:
- Center \( M(29, 0) \) means \( h = 29 \) and \( k = 0 \).
- Radius \( r = 20 \).

The equation becomes:
\[
(x - 29)^2 + y^2 = 20^2
\]
\[
(x - 29)^2 + y^2 = 400
\]
This is the equation of the circle.

### 2. **Finding Point \( C \)**:
From the problem, point \( C \) is the intersection of the circle with the y-axis. On the y-axis, the x-coordinate is 0, so to find point \( C \), substitute \( x = 0 \) into the equation of the circle.

The equation of the circle is:
\[
(0 - 29)^2 + y^2 = 400
\]
\[
841 + y^2 = 400
\]
\[
y^2 = 400 - 841
\]
\[
y^2 = -441
\]
This results in a negative number under the square root, which implies that there is no real intersection of the circle with the y-axis in this case. Therefore, point \( C \) as described doesn't exist with the given values, but this could suggest a check on the values or configuration of the system.

Would you like me to check this step further or assist with a different approach?

### Additional Questions:
1. Would you like more clarification on why point \( C \) might not exist with these parameters?
2. Should we review the given values for any inconsistencies?
3. Would you like to explore alternative methods for finding point \( C \)?
4. Should we verify point \( B \) and \( M \) coordinates before proceeding?
5. Are there any other details in the image you'd like to examine?

### Tip:
Always double-check values or parameters like center and radius when results seem unexpected (like a negative value under the square root).

I found Point B and M. M is (29, 0) and B is (4, 0). I need to find the equation of a circle and Point C.

Learn how to find the equation of a circle with a given center and radius, and how to determine the intersection point on the y-axis. This problem involves key geometry concepts like the equation of a circle and distance formula. Suitable for Grades 9-12.

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