Answer
The graph of the ellipse is close to the graph of a circle
Work Step by Step
We are given the ellipse centred in origine:
$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$
$c^2=a^2-b^2$
As we are given that $\dfrac{c}{a}\rightarrow 0$, we have:
$\dfrac{\sqrt{a^2-b^2}}{a}\rightarrow 0$
This means that $a^2\approx b^2\Rightarrow a\approx b$
The equation of the ellipse becomes:
$\dfrac{x^2}{a^2}+\dfrac{y^2}{a^2}=1$
$x^2+y^2=a^2$
So when $\dfrac{c}{a}\rightarrow 0$, the graph of the ellipse gets closer to the graph of a circle.
See the graph:
