The intercept on the line y = x by the circle x 2 + y 2 - 2 x = 0 is A B . The equation of the circle with A B as a diameter is ……

Step-by-step solution

We have equation of line y = x and equation of circle x 2 + y 2 - 2 x = 0 Now, intersecting points of given line and circle x 2 + x 2 - 2 x = 0 ⇒ 2 x 2 - 2 x = 0 ⇒ 2 x x - 1 = 0 ⇒ x = 0,1 When x = 0 then y =0 when x =1 then y = 1 ∴ Coordinates of end points of diameter AB are (0, 0) and (1, 1) ∴ Required equation of circle with diameter AB x - 0 x - 1 + y - 0 y - 1 = 0 ⇒ x 2 - 2 + y 2 - y = 0 ⇒ x 2 + y 2 - x - y = 0