Question

Which point does not lie on the circle with center (0,0) and radius 6? (6,0) (-6,0) (0,6) (6, -6)

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} (h,k)=(0,0) \\ r=5 \\ The\text{ general equation of a circle centered on (h, k) with radius r is:} \\ (x-h)^2+(y-k)^2=r^2 \\ \text{The equation of a circle centered on the origin is given by}\colon \\ x^2+y^2=r^2 \\ \text{Let's substitute the various points into this equation, we have:} \\ 6^2+0^2=6^2(\text{True)} \\ -6^2+0^2=6^2(\text{True)} \\ 0^2+6^2=6^2(\text{True)} \\ 6^2+(-6^2)=6^2(\text{False)} \end{gathered}`

Therefore, we see that point (6, -6) does not lie on the circle with center (0, 0) and radius 6