Pre calc unit 9

Question 1

Equation of the circle

Answer 1

(x-h)^2 + (y-k)^2 = r^2

Question 2

Formula for horizontal elipse

Answer 2

(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1

Question 3

Formula for vertical elipse

Answer 3

(x-h)^2 / b^2 + (y-k)^2 / a^2 = 1

Question 4

What is the formula for c in an elipse

Answer 4

c^2 = a^2 - b^2

Question 5

What is the formula for eccentricity

Answer 5

e = c/a

Question 6

What is the horizontal equation for hyperbolas

Answer 6

(x-h)^2 / a^2) - (y-k)^2 / b^2 = 1

Question 7

Formula for vertical hyperbola

Answer 7

(y-k)^2 / a^2 - (x-h)^2 / b^2 = 1

Question 8

Formula for c in hyperbolas

Answer 8

c^2 = a^2 + b^2

Question 9

Formula for vertical parabola
rules for p

Answer 9

(x-h)^2 = 4p(y-k)
opens up if p>0
opens down if p<0

Question 10

Formula for horizontal parabola
rules for p

Answer 10

(y-k)^2 = 4p(x-h)
opens right if p>0
opens left if p<0

Question 11

What is the
a. Distance formula
b. Midpoint formula
c. what shape are they generally used for

Answer 11

a. square root of: (x1-x2)^2 + (y1-y2)^2
b. (x1+x2/2) , (y1+y2/2)
c. circles but all shapes too

Question 12

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

Answer 12

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

Question 13

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

Answer 13

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

Question 14

For hyperbolas what is the horizontal asymptote equation

Answer 14

y-k = +-b/a (x-h)

Question 15

For hyperbolas what is the vertical asymptote equation

Answer 15

y-k = +-a/b (x-h)

Question 16

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

Answer 16

a. |p|
b. latus rectum
focus
|4p|
c. 2p

Question 17

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

Answer 17

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

Question 18

What is the area of an ellipse?
Can you find the area of an hyperbola

Answer 18

piAB
no