Conic Sections

Question 1

straight line intersects at a fixed point and rotates about it

Answer 1

double right circular cone

Question 2

fixed point

Answer 2

vertex

Question 3

line that rotates around the vertex

Answer 3

generator

Question 4

fixed line, perpendicular to the base

Answer 4

axis

Question 5

perimeter base

Answer 5

directrix

Question 6

lateral surface of cone; consists of upper and lower

Answer 6

nappes

Question 7

a<b; angle between plane and axis (b) is greater than vertex angle (a)

Answer 7

ellipse

Question 8

plane perpendicular to axis; special type of ellipse

Answer 8

circle

Question 9

a=b; angle made by plane and axis is equal to the vertex angle; open curve

Answer 9

parabola

Question 10

plane intersects one nappe - a>=b
intersects 2 nappes - a>b
disjoint curves

Answer 10

hyperbola

Question 11

intersects at vertex
ellipse becomes a point
parabola is a line
hyperbola becomes two intersecting lines

Answer 11

degenerate

Question 12

circle standard equation

Answer 12

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

Question 13

diameter of a circle

Answer 13

2r

Question 14

area of a circle

Answer 14

πr^2

Question 15

point at which the curve touches with the x-axis

Answer 15

tangent

Question 16

horizontal parabola standard equation

Answer 16

p: (x-h)^2 = 4p (y-k)
-p: quadratic function

Question 17

vertical parabola standard equation

Answer 17

-p: (y-k)^2 = 4p (x-h)
p: not a function

Question 17

parabola
end points of latus rectum

Answer 17

2|p|

Question 17

ellipses standard equation
horizontal major axis

Answer 17

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

Question 17

ellipses standard equation
vertical major axis

Answer 17

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

Question 17

parabola
focal distance; distance from f to v

Answer 17

p

Question 18

ellipses
distance from center to one vertex

Answer 18

a

Question 19

ellipses
distance from center to one co-vertex

Answer 19

b

Question 19

ellipses
distance from center to one focus

Answer 19

c

Question 20

ellipses equation for a, b, c

Answer 20

a^2 - b^2 = c^2

Question 21

hyperbola standard equation horizontal transverse axis

Answer 21

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

Question 22

hyperbola standard equation vertical transverse axis

Answer 22

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

Question 23

hyperbola distance from center to vertex

Answer 23

a

Question 24

hyperbola conjugate axis

Answer 24

2b

Question 25

hyperbola center to focus

Answer 25

c

Question 26

hyperbola equation for a, b, c

Answer 26

c^2 = a^2 + b^2

Question 27

hyperbola asymptotes

Answer 27

y - k = m (x-h)