Pre calc unit 9 Flashcards
Equation of the circle
(x-h)^2 + (y-k)^2 = r^2
Formula for horizontal elipse
(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1
Formula for vertical elipse
(x-h)^2 / b^2 + (y-k)^2 / a^2 = 1
What is the formula for c in an elipse
c^2 = a^2 - b^2
What is the formula for eccentricity
e = c/a
What is the horizontal equation for hyperbolas
(x-h)^2 / a^2) - (y-k)^2 / b^2 = 1
Formula for vertical hyperbola
(y-k)^2 / a^2 - (x-h)^2 / b^2 = 1
Formula for c in hyperbolas
c^2 = a^2 + b^2
Formula for vertical parabola
rules for p
(x-h)^2 = 4p(y-k)
opens up if p>0
opens down if p<0
Formula for horizontal parabola
rules for p
(y-k)^2 = 4p(x-h)
opens right if p>0
opens left if p<0
What is the
a. Distance formula
b. Midpoint formula
c. what shape are they generally used for
a. square root of: (x1-x2)^2 + (y1-y2)^2
b. (x1+x2/2) , (y1+y2/2)
c. circles but all shapes too
For ellipses:
a. What is the major axis, and how long is it
b. What is the minor axis, and how long is it
c. what are the vertices, and how far are they from the center
d. what are the co-vertices, and how far are they from the center
e. how far are the foci from the center
a. Longer axis of symmetry, 2a
b. shorter axis of symmetry, 2b
c. end points of the major axis, a
d. end points of the minor axis, b
e. c
For hyperbolas:
a. the center is the _____ of the foci
b. The vertices are ____ from the center
c. the co-vertices are _____ from the center
d. what is the transverse axis, and how long is it
e. what is the conjugate axis, and how long is it
f. the foci are _____ from the center
a. midpoint
b. a
c. b
d. it connects the vertices and is 2a long
e. it connects the co-vertices and is 2b long
f. c
For hyperbolas what is the horizontal asymptote equation
y-k = +-b/a (x-h)
For hyperbolas what is the vertical asymptote equation
y-k = +-a/b (x-h)
For parabolas:
a. the vertex is ____ away from the focus and the directrix
b. the ____ ______ is a segment that passes through the ____ with endpoints on the parabolic curve and has a length of _____
c. the focus and latus rectums are _____ away from each other
a. |p|
b. latus rectum
focus
|4p|
c. 2p
What is the discriminant?
What do each of the variables correspond with
a. using the discriminant how do you know if somethings a circle
b. using the discriminant how do you know if somethings a ellipse
c. using the discriminant how do you know if somethings a parabola
d. using the discriminant how do you know if somethings a hyperbola
B^2 - 4AC
B is always 0 A goes with x^2 C goes with y^2
a. if its < 0 and A=C
b. if its < 0 and A does not = 0
c. of it = 0
d. if its > 0
What is the area of an ellipse?
Can you find the area of an hyperbola
piAB
no
