Conic Section Formulas Flashcards
Distance formula
Sq. root of (x2 - x1)^2 + (y2 - y1)^2
Midpoint formula
(X1 + X2/2, y1 + y2/2)
Up and down parabola equation
Y= a(x - h)^2 + k
Left and right parabola equation
X= a(y - k)^2 + h
Vertex of parabolas
(h, k)
Axis of symmetry of up and down parabola
X = h
Focus of up and down parabola
(h, k + 1/4a)
Directrix of up and down parabola
y = k - 1/4a
Axis of symmetry of right and left parabola
Y = k
Focus of left and right parabola
(h + 1/4a, k)
Directrix of left and right parabola
X = h - 1/4a
If a<0 in a parabola
The parabola is either left or down
If a>0 in a parabola
The parabola is either up or right
Standard circle formula
(x - h)^2 + (y - k)^2 = r^2
Center of a circle
(h, k)
Radius of a circle
r
Standard eq. Horizontal ellipse
(x - h)^2/ a^2 + (y - k)^2/b^2 = 1
Foci of horizontal ellipse
(h +/- c, k)
Length of major axis of ellipse
2a
Length of minor axis of ellipse
2b
Relationship of a/b/c of ellipse
A^2 - b^2 = c
Standard eq. Of vertical ellipse
(x - h)^2/b^2 + (y - k)^2/ a^2 = 1
Foci of vertical ellipse
(h, k+/- c)
Standard eq. Of horizontal hyperbolas
(x - h)^2/a^2 - (y - k)^2/ b^2 = 1
Vertices of horizontal hyperbola
(h +/- a, k)
Foci of horizontal hyperbolas
(h +/-, k)
Co- vertices of hyperbola
Same as vertices only a is b
Length of transverse axis of hyperbola
2a
Length of conjugate axis of hyperbola
2b
Relationship between a b and c of hyperbola
a^2 + b^2 = c^2
Standard equation of vertical hyperbola
(y - k)^2/ a^2 - (x - h)^2/ b^2 = 1
Vertices of vertical hyperbola
(h, k +- a)
Foci of vertical hyperbolas
(h, k+- c)
Slope of horizontal asymptotes
+- b/a
Slope of vertical asymptotes
+- a/b
