Question 262418
Here is the original equation
(i) {{{x^2+y^2+8x+2y+13=0}}}
step 1 - rearrange the terms so that x's are grouped and y's are grouped together.
(ii) {{{x^2 + 8x + _____ + y^2 + 2y + _____ = -13 + _____ + _____}}}
the blanks are waiting for certain numbers
step 2 - take 1/2 of the middle terms and square it
(1/2)*8 = 4 -> 4^2 = 16
(1/2)*2 = 1 -> 1^2 = 1
so, we get
(iii) {{{x^2 + 8x + 4^2 + y^2 + 2y + 1^2 = -13 + 4^2 + 1^2}}}
notice that the blanks were filled in with the squared numbers.
step 3 - rewrite the x any y trinomial as a binomial squared. Also, simplify the right side to get
(iv) {{{(x+4)^2 + (y + 1)^2 = 4}}}
notice that the constant is 1/2 the middle term.
we have everything we need to find center and radius.
center = (h,k) = (-4,-1)
radius = 2