Find the standard form for the equation of a circle ( x − h ) 2 + ( y − k ) 2 = r 2 with a diameter that has endpoints ( − 2 , − 8 ) and ( 6 , 4 ) . h = k = r =

Answer 1

Using two endpoints to find center (midpoint formula) and using one endpoint and midpoint to find radius (distance formula).

h= Xm = (x1+x2)/2 = (-2+6)/2=2

k= Ym = (y1+y2)/2 = (-8+4)/2= -2

r= sqrt((x1-Xm)^2+(y1-Ym)^2)= sqrt(( 2+2)^2 + (-2+8)^2) = sqrt(52)

Equation: (x-2)^2 + (y+2)^2 = 52

Answer 2

Determine distance between the two points.

One-half the distance is the radius, r

Determine the midpoint between the two points

That is the center, (h, k), of the circle.