how do you find the formula for the top half of a circle w/ center (-1,2) radius 3
The general equation for a circle is x^2 + y^2 = r^2, where r is the radius. The center of this circle is the origin. To move it to some other point, we'll call it (h, k), replace x with (x - h) and y with (y - k) in the equation above. You have h, k, and the radius, so just plug in and you're done. Now, to restrict this to the top half, solve for y. The other side of the equation will have a square root with +/- in front of it. One sign is the upper half, the other sign is the lower half. That give you enough to go on?
Thank you for responding! I don't want to move the circle, I am just trying to find the formula for the function. The answer is y=2+√9-(x+1)^2 Does that make sense to you?
Actually, you do want to move the circle -- you want the center at (-1, 2) instead of at (0, 0). So -1 is h and 2 is k: (x- (-1))^2 + (y - 2)^2 = 3^2. Solving that for y and taking only the positive square root will give you the result above.
Join our real-time social learning platform and learn together with your friends!