Question 329434
a){{{(h-12)^2+(k+1)^2=R^2}}}
{{{h^2-24h+144+k^2+2k+1=R^2}}}
1.{{{h^2+k^2-24h+2k+145=R^2}}}
{{{(h-6)^2+(k+3)^2=R^2}}}
{{{h^2-12h+36+k^2+6k+9=R^2}}}
2.{{{h^2+k^2-12h+6k+45=R^2}}}
{{{(h-4)^2+(k-3)^2=R^2}}}
{{{h^2-8h+16+k^2-6k+9=R^2}}}
3.{{{h^2+k^2-8h-6k+25=R^2}}}
Equate eq. 1 and eq. 2,

{{{h^2+k^2-24h+2k+145=h^2+k^2-12h+6k+45}}}
{{{-24h+2k+145=-12h+6k+45}}}
{{{-12h-4k=-100}}}
4.{{{3h+k=25}}}
Equate eq. 1 and eq. 3,
{{{h^2+k^2-24h+2k+145=h^2+k^2-8h-6k+25=R^2}}}
{{{-24h+2k+145=-8h-6k+25}}}
{{{-16h+8k=-120}}}
5.{{{2h-k=15}}}
Add eq. 4 and eq. 5 to eliminate k.
{{{3h+k+2h-k=25+15}}}
{{{5h=40}}}
{{{highlight(h=8)}}}
Then use either eq. 4 or 5 to solve for h.
{{{16-k=15}}}
{{{highlight(k=1)}}}
Finally solve for R,
{{{(h-12)^2+(k+1)^2=R^2}}}
{{{(8-12)^2+(1+1)^2=R^2}}}
{{{16+4=R^2}}}
{{{R=sqrt(20)}}}
{{{highlight(R=2sqrt(5))}}}
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{{{highlight_green((x-8)^2+(y-1)^2=20)}}}
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b)
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Circle, points, and two lines plotted.
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{{{drawing(300,300,-2,12,-7,7, circle(8,1,sqrt(20)),circle(8,1,0.15),circle(12,-1,.3),circle(6,-3,.3),circle(4,3,.3),grid(1),graph(300,300,-2,12,-7,7,0,1,2x-1))}}}