Answer:
<u><em>(x+2)^2 + (y-6)^2 = 41</em></u>
Step-by-step explanation:
The equation for a circle is (x-h)^2+(y-k)^2=r^2
So first, it is known that the circle's center is at (-2,6), Therefore, this can be filled in:
(x+2)^2+(y-6)^2=r^2
Next, we need to find the radius, and one of the points is already known, being (-6, 1)
With this, find the distance between these two points by doing the Pythagorean Theorem, a^2+b^2=c^2. The a^2 would be the x value changed and the b^2 would be the y value changed between the two numbers. Note that this is interchangeable.
To find a:
-2 to -6 = change of 4
To find b:
6 to 1 = change of 5
Next, write out the equation for this:
4^2+5^2=c^2
16+25=c^2
41=c^2
c = √41
The radius would be √41, so the equation can now be completed. Since c will be brought to the second power, this will cancel out the square root.
(x+2)^2 + (y-6)^2 = 41
Hope that helps.
