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Phantasy [73]
3 years ago
13

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

Mathematics
1 answer:
GREYUIT [131]3 years ago
7 0
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

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