Chapter 9 Flashcards
point slope formula
y-y(1)= m (x-x(1))
(x-h)^2=4p(y-k)
opens up or down
a parabola opens up if
p>0
a parabola opens down if
p<0
(y-k)^2=4p(x-h)
opens right or left
a parabola opens right if
p>0
a parabola opens left if
p<0
focus
P from vertex
inside parabola
distance formula
d=sq root of (y1-y2)^2 + (x1-x2)^2
d1=d2
distance from given point to focus=distance from focus to tangent line’s y/x intercept
how to tell if ellipse/circle
B^2 -4AC<0
how to tell if parabola
B^2-4AC=0
how to tell if hyperbola
B^2-4AC>0
how to tell if hyperbola transverse axis is horizontal (right and left)
[(x-h)^2/a^2] -[(y-k)^2/b^2]
x comes first
how to tell if hyperbola transverse axis is vertical (top and bottom)
[(y-k)^2/a^2]-[(x-h)^2/b^2]
hyperbola: foci are ___ units from center
c units from center
c^2 = a^2 + b^2
foci = (h+/- c, k)
(h, k+/-c)
slope of asymptotes in hyperbola
and how to find asymptotes
if vertical:
y=+/- (b/a) • (x-h)
if horizontal:
y=+/- (a/b) • (x-h)
general form of conics
Ax^2+Cy^2+Dx+Ey+F=0
circle, using general form
A=C
parabola, using general form
AC=0
ellipse, using general form
AC>0
hyperbola,using general form
AC<0
find angle in rotation
cot 2a= A-C/B
what does x= in rotation of conics
x= (x1)cos a - (y1)sin a
what does y= in a rotation of conics
y=(x1) sin a + (y1) cos a
distance “a” in an ellipse
distance from center to vertice
under x when the major axis is horizontal, under y when the major axis is vertical
distance “b” in an ellipse
distance from center to covertice (shorter length)
under y when the major axis is horizontal, under x when the major axis is vertical
foci in an ellipse
lie on the major axis
c distance from center
c^2= a^2 - b^2
ellipse - major axis horizontal
[(x-h)^2/a^2] + [(y-k)^2/b^2]
ellipse - major axis is vertical
[(x-h)^2/b^2] + [(y-k)^2/a^2]
eccentricity of an ellipse
the closer “e” is to zero, the more oval, or eccentric, the ellipse is
e=c/a
distance a in hyperbola
distance from center to vertex
area of an ellipse
area= pi • ab
polar equations in parametric form:
x=?
x=f(t) *[cos(t)]
polar equations in parametric form:
y=?
y=f(t)*[sin(t)]
special polar graph: limacon
a/b <1
Limacons Inner Loop
special polar graphs: limacon
a/b=1
limacon, cardioid
special polar graph: limacon
1<a></a>
dimpled limacon
special polar graphs: limacon
a/b>=2
convex limacon
special polar graphs: rose curves
r=acos(nx) / r=asin(nx)
n is odd
n petals if odd
special polar graphs: rose curves
r=acos(nx) / r=asin(nx)
n=even
2n petals if even
special polar graphs: circles
if sin
if cos
if sin=shifted up or down
if cos=shifted right or left
how to use e to tell if ellipse
if e<1, ellipse
how to use e to tell if parabola
e=1
how to use e to tell if hyperbola
e>1
polar equations of conics
r= (ep)/(1+- ecos(x))
or
r=(ep)/(1+- esin(x))
how to tell if there’s a horizontal directrix above the pole
r=ep/1+esin(x)
how to tell if there’s a horizontal directrix below the pole
r=ep/1-esin(x)
how to tell if there’s a vertical directrix to right of pole
r=ep/1+ecos(x)
how to tell if there’s a vertical directrix to left of pole
r=ep/1-ecos(x)
