Question 1039382

Find equation of the circle whose diameter has endpoints (1,-6) and (-9,0)
<pre><b><font size=4>1<sup>st</sup>:<u> Find the CENTER, which is the midpoint of the diameter</u>
({{{matrix(1,3, (x[1] + x[2])/2, ",", (y[1] + y[2])/2)}}}) =====> ({{{matrix(1,3, (1 + - 9)/2, ",", (- 6 + 0)/2)}}}) =====> {{{matrix(1,5, "(", - 4, ",", - 3, ")")}}} =====> {{{matrix(1,5, "(", h, ",", k, ")")}}} 

2<sup>nd</sup>:<u> Use the CENTER, or (h, k) and one of the 2 points to determine {{{r^2}}}, or the {{{(radius)^2}}}</u>
{{{(x - h)^2 + (y - k)^2 = r^2}}}
{{{(- 9 - - 4)^2 + (0 - - 3)^2 = r^2}}}
{{{(- 9 + 4)^2 + (3)^2 = r^2}}}
{{{(- 5)^2 + 3^2 = r^2}}}
{{{25 + 9 = r^2}}}____{{{34 = r^2}}}

3<sup>rd</sup>:<u> Use the CENTER, or (h, k) and {{{r^2}}} to form the equation of the circle</u>
{{{(x - h)^2 + (y - k)^2 = r^2}}}
{{{(x - - 4)^2 + (y - - 3)^2 = 34}}} ------- Substituting (- 4, - 3) for (h, k), and 34 for {{{r^2}}}
{{{highlight_green(matrix(1,2, "Equation:", (x + 4)^2 + (y + 3)^2 = 34))}}}