# How do you graph x^2+y^2=4?

Feb 28, 2016

See the explanantion

#### Explanation:

This is the equation of a circle with its centre at the origin.

Think of the axis as the sides of a triangle with the Hypotenuse being the line from the centre to the point on the circle.

By using Pythagoras you would end up with the equation given where the 4 is in fact ${r}^{2}$

To obtain the plot points manipulate the equation as below:

Given:$\text{ "x^2+y^2=r^2" "->" } {x}^{2} + {y}^{2} = 4$

Subtract ${x}^{2}$ from both sides giving:

$\text{ } {y}^{2} = 4 - {x}^{2}$

Take the square root of both sides

$\text{ } y = \sqrt{4 - {x}^{2}}$

Now write it as

$\text{ } y = \pm \sqrt{4 - {x}^{2}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Calculate and plot a series of points using first the positive version of this equation then repeat using the negative side.

You should then get something that looks like:

The axis scale in mine do not exactly match in scale, so the plot looks a little flattened!