The intercept on the line y=x by the circle x2+y2−2x=0, is AB. The equation of the circle on AB as a diameter, is
A
x2+y2=x+y
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x2+y2−x+y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2+y2+x+y=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x2+y2+x=y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Bx2+y2=x+y Solving given line and the circle, x2+x2−2x=0⇒x=0,1 Thus coordinates of A and B are (0,0) and (1,1) respectively, Hence equation of circle with AB as diameter is given by, x(x−1)+y(y−1)=0⇒x2+y2=x+y