the equation of the circle with chord 2x=y of the circle x^2+y^2=10x as it's diameter

The chord and circle will intersect at two points.

When y = 2x, we have

x² + (2x)² = 10x 

5x² = 10x 

5x(x - 2) = 0

Therefore, x = 0, 2

So, y = 0, 4

Thus, the points of intersection will be (0, 0) and (2, 4).

So, the end points of the diameter are (0, 0) and (2, 4)

Therefore, the equation of circle will be

(x - 0)(x - 2) + (y - 0)(y - 4) = 0

x² - 2x + y² - 4y = 0

x² + y² - 2x - 4y = 0