If `y=2x` is a chord of the circle `x^2+y^2-10 x=0` , find the equation of a circle with this chord as diameter.

Explanation

To solve the problem step by step, we need to find the equation of a circle that has the chord \( y = 2x \) as its diameter, given that this chord is part of the circle defined by the equation \( x^2 + y^2 - 10x = 0 \).

### Step 1: Rewrite the Circle's Equation
The given equation of the circle is:
\[ x^2 + y^2 - 10x = 0 \]
We can rewrite this equation in standard form by completing the square for the \( x \) terms.
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