Conics

Question 1

Right opening parabola

Answer 1

(y-k)² = 4a(x-h)

Question 2

Left opening parabola

Answer 2

(y-k)² = -4a(x-h)

Question 3

Standard parabola

Answer 3

(x-k)² = 4a(y-k)

Question 4

Inverted parabola

Answer 4

(x-k)² = -4a(y-k)

Question 5

Standard parabola focus

Answer 5

(h+a, k)

Question 6

Inverted parabola focus

Answer 6

(h-a, k)

Question 7

Right opening parabola foci

Answer 7

(h, k+a)

Question 8

Left opening parabola foci

Answer 8

(h, k-a)

Question 9

Horizontal parabola directrix

Answer 9

x = h±a (a is negative when opening left)

Question 10

Vertical parabola directrix

Answer 10

x = k±a (a is negative when opening down)

Question 11

Horizontal ellipse

Answer 11

(x-h)²/a² + (y-k)²/b² = 1

Question 12

Vertical ellipse

Answer 12

(x-h)²/b² + (y-k)²/a² = 1

Question 13

Vertical ellipse foci

Answer 13

(h, k±c)

Question 14

Horizontal ellipse foci

Answer 14

(h±c, k)

Question 15

Horizontal ellipse vertices

Answer 15

(h±a, k)

Question 16

Vertical ellipse vertices

Answer 16

(h, k±a)

Question 17

b

Answer 17

Length from center of an ellipse to the edge of the ellipse along the minimal axis

Question 18

a

Answer 18

Distance from vertex to focus and/or directrix of a parabola

OR

Distance from center of an ellipse to either vertex along the maximal axis

Question 19

h

Answer 19

x-coordinate of the vertex of a parabola

OR

x-coordinate of the center of an ellipse

Question 20

k

Answer 20

y-coordinate of the vertex of a parabola

OR

y-coordinate of the center of an ellipse

Question 21

c

Answer 21

b² = a² + c²

(might be some kind of rectum but we don’t need to know that)

Question 22

finishing the square

Answer 22

group terms by variable

add b²/4a to each variable group

a = leading coefficient (make this 1 before completing)
b = coefficient of x

remove negative terms from each group

you can figure it out from here

Question 23

latus rectum parabola

Answer 23

line through the focus parallel to the directrix

Question 24

points that define the latus rectum parabola

Answer 24

2a away from the focus (remember the l.r. is parallel to the directrix)