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

1 Answer
Tony B
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:#" "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:

Tony B

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

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