Given, equation of circle is x2+y2=2 ..........(i) Taking derivative w.r.t.x. 't' on both sides 2x
dx
dt
+2y
dy
dt
=0⇒x
dx
dt
+y
dy
dt
=0 If abscissa and ordinate increases at the same rate, we have
dx
dt
=
dy
dt
x
dx
dt
+y
dx
dt
=0⇒
dx
dt
(x+y)=0 Since,
dx
dt
≠0 ⇒x+y=0⇒x=−y ...........(ii) Solving Eqs. (i) and (ii), we get x2+(−x)2=2⇒x=±1 For x=1,y=−1 and x=−1,y=1 Required point are (1,−1) and (−1,1).