e

if y = 2x is a chord of the circle x^{2} + y^{2} - 10x =0

find the equation of the circle with this chord as diameter

since y=2x is the chord of the circle

let the chord be AB, so we will find the intersection point of line y=2x and circle (1).

therefore x=0 or x=2.

y=0 or y=4

thus the coordinates of end points of the chord is A (0,0) and B(2,4).

now consider these points A and B as the end points of diameter of a circle.

the mid-point of AB is the center of the circle =

the distance AB is the length of the diameter AB.

AB=

thus the radius of the circle is

thus the equation of the circle is

which is the required equation of the circle.

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