Home / Assignment Help / The equation =+y3115 is solved in several steps below. For each step, choose the reason that best justifies it.

The equation =+y3115 is solved in several steps below. For each step, choose the reason that best justifies it.

So hmm check the picture below, that’s about the circle and the endpoints, but notice, the endpoints make up a segment, namely the diameter of the circle, well…. let’s see how long that is, because, the radius is half the diameter

bf textit{distance between 2 points}\ quad \
begin{array}{lllll}
&x_1&y_1&x_2&y_2\
%  (a,b)
&({{ 7}}quad ,&{{ 3}})quad 
%  (c,d)
&({{ 7}}quad ,&{{ -5}})
end{array}qquad 
%  distance value
d = sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\
d=sqrt{(7-7)^2+(-5-3)^2}implies d=sqrt{0+(-8)^2}implies d=8
\\\
textit{the radius is half that, so is }boxed{r=4}

now.. hmmm notice, the midpoint of the diameter, is the center of the circle, let’s check that one out

bf textit{middle point of 2 points }\ quad \
begin{array}{lllll}
&x_1&y_1&x_2&y_2\
%  (a,b)
&({{ 7}}quad ,&{{ 3}})quad 
%  (c,d)
&({{ 7}}quad ,&{{ -5}})
end{array}qquad 
left(cfrac{{{ x_2}} + {{ x_1}}}{2}quad ,quad cfrac{{{ y_2}} + {{ y_1}}}{2} right)
\\\
left(cfrac{{{ 7+7}}}{2}quad ,quad cfrac{{{ -5}} + {{ 3}}}{2} right)implies left( cfrac{14}{2} , cfrac{-2}{2} right)implies boxed{(7,-1)}

now.. that we know what the center is, and what the radius is, well

bf textit{equation of a circle}\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
qquad 
begin{array}{lllll}
center (&{{ h}},&{{ kquad }})qquad 
radius=&{{ r}}\
&7&-1&4
end{array}

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