More Conics

We learned thr conversion between general form conics and standrd conics.

Ax^2 + Bxy + Cx^2 + Dx + Ey + F = 0


complete the square:

you take: x^2 + 4x + 4

We can take a square and
(x+2)(x+2)
(x+2)^2

If we try to enter (X^2 + y^2 + 6x - 8y) = 11 into graphimatica, it will not map the equation because it cannot take the data. We use this form after we complete the square

(X^2 + y^2 + 6x - 8y) = 11
(x^2+6x+9)(y^2-8y+16) = 11 + 9 + 16
(x+3)^2 + (y - 4)^2 = 36

Using the general form:

(x-h)^2+(y-k)^2= r^2
(h,k) = center r = radius
enter (x+3)^2+(y-4)^2= 36