Question

6.) 4x² + 4y² = 1

Explanation:

Step1: Rewrite the equation in standard form

Divide the entire equation $4x^{2}+4y^{2}=1$ by 4. We get $x^{2}+y^{2}=\frac{1}{4}$.

Step2: Identify the properties of the circle

The standard - form of a circle equation is $(x - a)^{2}+(y - b)^{2}=r^{2}$, where $(a,b)$ is the center of the circle and $r$ is the radius. In the equation $x^{2}+y^{2}=\frac{1}{4}$, we have $a = 0$, $b = 0$ and $r=\frac{1}{2}$ (since $r^{2}=\frac{1}{4}$, then $r=\sqrt{\frac{1}{4}}=\frac{1}{2}$).

Answer:

This is the equation of a circle centered at the origin $(0,0)$ with radius $r = \frac{1}{2}$.