Question

Use the distance formula to write an equation for all points that are 5 units from (0,0). Sketch a graph showing these points.

Answer 1

We know from the Pythagorean theorem that:
\[x^2+y^2=D^2\] Where \(D\) is distance.

So then
\[x^2+y^2=5^2=25\]

Answer 2

Distance formula:
\[D = \sqrt{(y₂-y₁)² + (x₂-x₁)²}\]

Let's say that the initial point (x₁, y₁) is (0,0). We're given that D=5:

Answer 3

You have the equation of:
\[x^2+y^2=25\] Or
\[y=\pm\sqrt{25-x^2}\] Which is actually the equation of a circle with a radius of five centred at \((0,0)\)