Question 1079002
So use the general equation of the circle,
{{{(x-h)^2+(y-k)^2=R^2}}}
Since you know the center is on the y-axis, then {{{h=0}}}
{{{x^2+(y-k)^2=R^2}}}
So using the two points,
{{{4^2+(2-h)^2=R^2}}}
{{{16+(2-h)^2=R^2}}}
and
{{{(-6)^2+(-2-h)^2=R^2}}}
{{{36+(-2-h)^2=R^2}}}
Setting them equal to each other,
{{{16+(2-h)^2=36+ (-2-h)^2 }}}
{{{16+4-4h+h^2=36+4+4h+h^2}}}
{{{-8h=20}}}
{{{h=-20/8}}}
{{{h=-5/2}}}
So then use either point to solve for R.
{{{16+(2-(-5/2))^2=R^2}}}
{{{16+(4/2+5/2)^2=R^2}}}
{{{16+(9/2)^2=R^2}}}
{{{64/4+81/4=R^2}}}
{{{R^2=145/4}}}
So then,
{{{highlight(x^2+(y+5/2)^2=145/4)}}}
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*[illustration da3.JPG].