Question 883631
Find the radius using Distance Formula for points (-1,6) and the center(2,-1)....


There is an alternative.  The center and the given endpoint form a line.  The other endpoint is a point on this line.  Now, using Distance formula, and knowing the equation of this line, you are looking for the point this way:


D, (-1,6) to (2,-1) SAME AS  D, (x,y) to (2,-1).  

{{{sqrt((6-(-1))^2+(-1-2)^2)=sqrt((x-2)^2+(y-(-1))^2)}}}
{{{sqrt((49)^2+(9)^2)=sqrt((x-2)^2+(y+1)^2)}}}
{{{sqrt(130)=sqrt(x-2)^2+(y+1)^2)}}}
{{{130=(x-2)^2+(y+1)^2}}}---actually this is just the equation of the circle.


The line containing given endpoint and circle center:
{{{m=(6+1)/(-3)}}}
{{{m=-7/3}}}
y=mx+b
b=y-mx
{{{b=-1-(-7/3)*2}}}
{{{-1-(-14/3)}}}
{{{14/3-3/3}}}
{{{b=11/3}}}
-
{{{highlight_green(y=-(7/3)x+11/3)}}}.


WHAT NEXT TO DO?
Substitute for y in the circle equation, simplify, and solve for x.  You will get two values.  The one you are looking for is the solution OTHER THAN x=-1.  Now, use it to find y.