Question

Find the equation of the circle that has a diameter with endpoint located at (-5,-3) and (-11,-3).

Answer 1

check the picture below.

you can pretty much, without having to use the distance formula, see the diameter is 6 units long, thus the radius is half that or 3 then.

now, without having to use the midpoint formula, if we move from either endpoint inwards 3 units, we'll end up at the center, -5 -3, is just -8, so the center will be at -8, -3.


`\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad center~~(\stackrel{-8}{{{ h}}},\stackrel{-3}{{{ k}}})\qquad \qquad radius=\stackrel{3}{{{ r}}} \\\\\\\ [x-(-8)]^2+[y-(-3)]^2=3^2\implies (x+8)^2+(y+3)^2=9`