Conics

how do you tell which equations are for which graphs?

circle - A = B

ellipse - A and B have same sign

hyperbola - A and B have opposite signs

parabola - A and B = 0

equation of circle

(x-h)²+(y-k)²=r²

equation of ellipse

conic form: Ax²+By²+Cx+Dy+E=0

Graphing form: x²/a²orb² + y²/a²orb² = 1

when is the ellipse longer horizontally

when a is under x (x²/a² + y²/b² = 1)

when is the ellipse longer vertically

when a is under y (x²/b² + y²/a² = 1)

equation to find foci of ellipse

c²=sqrt a²-b²

equation of hyperbola

Conic Form: Ax²+By²+Cx+Dy+E=0 (A and B have to be opposite signs)

Graphing Form: (x-h)²/a²-(y-k)²/b²=1 or (y-k)²/a²-(x-h)²/b²=1

when does a hyperbola open sideways?

when x-term is positive

when does a hyperbola open upward/downword?

when y-term is positive

equation to find foci of hyperbola

c=sqrt a²+b²

what is the equation of the asymptote for a hyperbola that opens sideways?

y-k=±b/a(x-h)

what is the equation of the asymptote for a hyperbola that opens upward/downword?

y-k=±a/b(x-h)

equation of parabola

(x-h)² = ±4p(y-k) or (y-k)² = ±4p(x-h)

when does a parabola open upward?

when (x-h) is squared and when 4p is positive

when does a parabola open downward?

when (x-h) is squared and when 4p is negative

when does a parabola open to the right?

when (y-k) is squared and when 4p is positive

when does a parabola open to the left?

when (y-k) is squared and when 4p is negative

what is p?

the distance from the vertex to the focus and directrix