Problem of sketching a circle

Question

I've to solve a problem in which I've been given this equation: $x^2 + y^2 = 4$ and I've to sketch a circle which is the locus of the equation. Here $2$ is the radius $r$ of the circle. $2$ doesn't have any unit with it, like "cm" or "m". So should I open my compass to "2" equal units of $x$-axis or $y$-axis? or to $2$ cm? Sorry this question is unsophisticated, but I've to solve the problem, so please help me.

Answer 1

The equation of a circle, centered at the origin, is given by:

$$x^2 + y^2 = r^2$$ where $r$ is the radius.

So your equation is $$x^2 + y^2 = 4 = (2)^2$$

So what is $r$, the radius?

$r$, like $x, y$ are simply measured in "units"; there is no specific unit attached to this.

Your circle represents all points of distance $r$ from the origin. So set your compass to $2$ units, calibrated to match the scale of the unit-tics along the x, or y axis. (You can use whatever scale you prefer to do this: graph paper comes in handy, just keep units/scale consistent), and pivot around the origin. Your circle should intersect the $x$-axis at $(2, 0),\; (-2, 0)$, the $y$-axis at $(0, 2), \; (0, -2)$, and all points $(x, y)$ such that $\sqrt{x^2 + y^2} = 2$