SOLUTION: Determine the equation of the circle defined by the given conditions a) (5,1) and (-3,3) are endpoints of a diameter Can you please help me out , thanks so much in advance:)

Algebra ->  Circles -> SOLUTION: Determine the equation of the circle defined by the given conditions a) (5,1) and (-3,3) are endpoints of a diameter Can you please help me out , thanks so much in advance:)      Log On


   

Question 800398: Determine the equation of the circle defined by the given conditions
a) (5,1) and (-3,3) are endpoints of a diameter
Can you please help me out , thanks so much in advance:)
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
If those are the endpoints of the diameter, then Midpoint Formula will give the coordinates for the center of the circle. You could then choose either given point and use the distance formula to calculate the radius of the circle.

Now, just plug the needed and found values into the Standard Form equation for a circle.

x=%285-3%29%2F2=1
y=%281%2B3%29%2F2=2
Center of Diameter is (1,2) meaning this is the center of the circle.

Radius: sqrt%28%285-1%29%5E2%2B%281-2%29%5E2%29=sqrt%284%5E2%2B%28-1%29%5E2%29=sqrt%2817%29

Using knowledge of standard form for a circle,
highlight%28%28x-1%29%5E2%2B%28y-2%29%5E2=17%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the equation of the circle defined by the given conditions
a) (5,1) and (-3,3) are endpoints of a diameter
***
equation of circle: (x-h)^2+(y-k)^2=r^2
To find center:
Use midpoint formula:(x1+x2)/2,(y1+y2)/2, with end points
=(5-3)/2,(1+3)/2=(1,2)=(x,y) coordinaes of center
..
Distance formula: d^2=(x1-x2)^2+(y1-y2)^2
to find radius, use distance formula with coordinates of center(1,2) and one endpoint(-3,3)
r^2=(-3-1)^2+(3-2)^2=16+1=17
equation of circle: (x-1)^2+(y-2)^2=17