Studied by 6 peopleConic section polynomial
Ax^2 + By^2 + Cx + Dy + E = 0
if the center is (0,0)
the equation is x^2 + y^2 = r^2
if the center is (h,k)
the equation is (x-h)^2 + (y-k)^2 = r^2.
horizontal ellipse (a,0) and (-a,0), a^2 > b^2
x^2 / a^2 + y^2 / b^2 = 1
vertical ellipse (0,a) and (0,-a), a^2 > b^2
x^2 / b^2 + y^2 / a^2 = 1
horizontal ellipse (h,k), a^2 > b^2
(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1
vertical ellipse (h,k), a^2>b^2
(x-h)^2 / b^2 + (y-k)^2 / a^2 = 1
Hyperbola (opens to the sides)
(x-h)^2 / a2 - (y-k)^2 / b^2 = 1
Hyperbola (opens up and down)
(y-k)^2 / a^2 - (x-h)^2 / b^2 = 1
Parabola
y = Ax^2 + Bx + C
If A < 0
the parabola opens downward and its vertex is the highest point on the parabola
If A > 0
then the parabola opens upward and its vertex is the lowest point on the parabola
ellipse
AB > 0
circle
A = B, A and B not equal to 0
parabola
A = 0 or B = 0, but not both
line
A = 0 and B = 0
hyperbola
AB < 0
Note
Flashcard