What is the equation for a circle with a center(8,-9) and passes through(21,22)

Question

aravindg · Answer

first find the radius of the circle

aravindg · Answer

Use distance formula

anonymous · Answer

how do i find the radius?

aravindg · Answer

Distance formula

aravindg · Answer

you have 2 points :

(8,-9)  ,(21,22)

anonymous · Answer

is there a formula to get the radius without graphing it

aravindg · Answer

ya radius 

= $$\sqrt{(21-8)^2+(22+9)^2}$$

whpalmer4 · Answer

notice that AravindG has done $\sqrt{(21-8)^2 + (22-(-9))^2} = \sqrt{(21-8)^2+(22+9)^2}$

aravindg · Answer

gt it ?

whpalmer4 · Answer

Once you have the radius, do you know the formula for a circle with center at $(h,k)$ and radius $r$?

anonymous · Answer

i dont know it

whpalmer4 · Answer

Okay, I can tell you the formula, or I can walk you through figuring it out, your choice...

whpalmer4 · Answer

you'll probably remember it better if we go through figuring it out, but it will take a little while.

whpalmer4 · Answer

Well, here's the formula:

$$(x-h)^2 + (y-k)^2 = r^2$$

Remember that a circle is just the set of points the same distance from its center.  If this formula looks suspiciously like the Pythagorean theorem to you, give yourself a gold star.  |dw:1369761200813:dw|  Subtracting $h$ and $k$ before squaring just move the center of the circle around.