<s>[INST] Is $\frac14 x^{2}+y^{2}=1$ equation of circle or not? Well, I have to draw this plane:
$$\frac{1}{4}x^{2}+y^{2}=1$$
How does this look like? Is this just a circle? If so I'm not sure how can I get rid of $\frac{1}{4}$ to make something like $(x-a)^{2}$ out of this.
 [/INST] No, you're equation is not the equation of a circle, but rather that of an ellipse.
A simple modification of the equation $$\frac{1}{4}x^{2}+y^{2}=1$$ gives you the canonical form of an ellipse: $$\dfrac {x^2}{a^2} + \frac{y^2}{b^2} = 1.$$
$$\frac{1}{4}x^{2}+y^{2}=1 \iff \frac {x^2}{4} + \frac{y^2}{1} = 1 \iff \frac{x^2}{(2)^2} + \frac {y^2}{(1)^2} = 1$$

$\qquad\qquad\frac 14 x^2 + y^2 = 1$
$\quad$ 
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