https://file.aiquickdraw.com/mathbot/file/1725708314951mr8xxg9v.jpg

The image shows a problem that appears to involve a differential equation and some constants. Let me transcribe and interpret the content for further analysis.

The problem involves:

- The diagram in the figure (presumably not shown in this upload) shows a straight line of the form \( y = mx + c \), where the constants \( m \) and \( c \) need to be determined.
- The governing equation is \( x^2 + y^2 = 3x \).
- Part (a) asks to solve the equation \( x^2 + y^2 = 3x \) by rearranging it into the form \( y = mx + c \) and determining values for \( m \) and \( c \).

### Step 1: Simplifying the equation \( x^2 + y^2 = 3x \)

1. Start with:
   \[
   x^2 + y^2 = 3x
   \]
   
2. Move all terms involving \( x \) to one side:
   \[
   y^2 = 3x - x^2
   \]

This represents a quadratic equation in \( x \), but we are looking for the form \( y = mx + c \), so we will explore further steps to solve this geometrically or algebraically for a straight line.

I will work out more details for you. Would you like a step-by-step breakdown of how to find the values of \( m \) and \( c \)? Let me know if there are additional questions regarding this process!

Solve the equation x^2 + y^2 = 3x by rearranging it to the form y = mx + c and determining m and c.

Learn how to rearrange the circle equation x^2 + y^2 = 3x into the form y = mx + c and find the slope and y-intercept. This problem covers key algebraic and geometric concepts, suitable for students in Grades 9-12.

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