put (x-6)^2+(y+7)^2=4 into ​(xminus​h)squaredplus​(yminus​k)squaredequalsrsquared. form

Answer 1

(x-6)^2 + (y+7)^2 = 4

To put this into the form (x-h)^2 + (y-k)^2 = r^2, we need to complete the square for both the x and y terms.

Starting with the x term, we have:

(x-6)^2 = x^2 - 12x + 36

Now, for the y term:

(y+7)^2 = y^2 + 14y + 49

Putting it all together:
x^2 - 12x + 36 + y^2 + 14y + 49 = 4

Rearranging and simplifying:
x^2 - 12x + y^2 + 14y = -81

Now, completing the square for x and y terms:
(x-6)^2 + (y+7)^2 = 81

Therefore, the equation (x-6)^2 + (y+7)^2 = 81 is in the form (x-h)^2 + (y-k)^2 = r^2.