COMEDK Exam 2017 Solved Paper

Let the required point be P(x1,y1)
The given curve is y=x2 . . . (i)
Differentiating Eq. (i) w.r.t. x, we get ‌

dy

dx

=2x⇒ Slope of tangent at P(x1,y1)=2x
But the slope of tangent at
‌P(x1,y1)=x‌-coordinate of ‌P
⇒2x1=x1⇒2x1−x1=0
⇒x1=0
As P(x1,y1) lies on the curve, we get
y1=x12⇒y1=0
Hence, the required point is (0,0).