Answer
$y-0=0(x-0)$ or $y=0$
Work Step by Step
Let the given point be $P(0,0)$.
Let the slope of the secant line from $P$ to a distinct point $Q(x,x^2)$ be $m$.
$\implies m=\dfrac{x^2-0}{x-0}$
Now simplify $ m=\dfrac{x^2-0}{x-0}$.
We get, $m=\dfrac{x^2}{x}=x$
if point $Q$ moves toward the point $P$ on the curve.
Then, $x$ approaches $0$.
That gives $m=0$
We know that if $Q$ gets closer to $P$, then the slope of secant gets closer to the slope of the tangent at $P$.
Hence, the slope of the tangent at $P$ is $0$.
Thus, the equation of the tangent line at $P$ can be written using point-slope form of a line as follows:
$y-0=0(x-0)$ or $y=0$
