if y = 2x is a chord of the circle x2 + y2 - 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.
thus the radius of the circle is
thus the equation of the circle is
which is the required equation of the circle.