Circles :3

Wazzzam yew guiseeee ;). I bet y'all all can't wait for school Monday, YAAAAYY.

Give an equation of a circle with end points on a diameter (2,1) (12,1).

We know that the standard form of a circle is: (x-h) ^2 + (y-k) ^2=r ^2.

Figuring out the distance from one end of the circle to the other, we will need the distance formula. (to figure out the diameter which will result in finding the radius).

D: √(x2-x1) ^2 + (y2-y1) ^2. You plug in the end points of your diameter (which was given) into this formula:

D: √(12-2) ^2 + (1-1) ^2 = √100 =10

D=10, R=5. So now we know that: (x-h) ^2 + (y-k) ^2 = 5 ^2

H and K in your standard formula is the center coordinates. To get this, you use the midpoint formula (hence center/midpoint).

Midpoint formula= (x1+x2 /2 , y1+y2 /2)

Plug in coordinates from original end points of diameter and get:

(2+12 /2 , 1+1 /2) = (7,1). When plugging this into your formula, remember that the coordinate’s signs change as shows:

Answer: (x-7) ^2 + (y-1) ^2 = 25 (25 comes from the radius which was found from using the distance formula)

Kthatisall.