Question

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

Answer 1

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:`" "x^2+y^2=r^2" "->" "x^2+y^2 =4`

Subtract `x^2` from both sides giving:

`" "y^2=4-x^2`

Take the square root of both sides

`" "y=sqrt(4-x^2)`

Now write it as

`" "y=+-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!