Conics Test

Question 1

How to tell if it is a circle

Answer 1

Both are squared and it equals a perfect square

Question 2

How to graph a circle with the center at (0,0)

Answer 2

Identify the center
Identify the radius (r) by taking the square root of the thing the equation equals
Plot points based on the radius
(x,y) (-x,y) (y,x) (-y,x)

Question 3

How to graph a circle with the center not at (0,0)

Answer 3

Identify the center
Identify the radius
Create two points with x as the same as the center and add and subtract the radius to y
Create two other points with y the same and add and subtract the radius to x

Question 4

How to write the equation of a circle

Answer 4

Center: (h,k)
Point: (x,y)
Find the radius with the equation
r= √(x-h)²+ (y-k)²
r²= that without the square root
Write the whole equation (x-h)² + (y-k)² =r²

Question 5

Horizontal Major Axis Ellipse Equation

Answer 5

(x-h)² / a² + (y-k)² / b² = 1

Question 6

Vertical Major Axis Ellipse Equation

Answer 6

(x-h)² / b² + (y-k)² / a² = 1

Question 7

Major Axis Ellipse

Answer 7

Both: 2a

Question 8

Minor Axis Ellipse

Answer 8

Both: 2b

Question 9

Horizontal Vertices Ellipse

Answer 9

(h +/- a, k)

Question 10

Vertical Vertices Ellipse

Answer 10

(h, k +/- a)

Question 11

Horizontal Co-vertices Ellipse

Answer 11

(h, k+/- b)

Question 12

Vertical Co-vertices Ellipse

Answer 12

(h +/- b, k)

Question 13

Horizontal Foci Ellipse

Answer 13

(h +/- c, k)

Question 14

Vertical Foci Ellipse

Answer 14

(h, k +/- c)

Question 15

Pythag. Relation Ellipse

Answer 15

c² = a² - b²

Question 16

Horizontal Hyperbola Transverse Axis Equation

Answer 16

(x-h)² / a² - (y-k)² / b² =1

Question 17

Vertical Hyperbola Transverse Axis Equation

Answer 17

(y-k)² / a² - (x-h)² / b² =1

Question 18

Focal Axis (Line through the Foci)

Answer 18

Both: 2c

Question 19

Hyperbola Line connecting vertices (transverse axis)

Answer 19

Both: 2a

Question 20

Line connecting co-vertices (conjugate axis)

Answer 20

Both 2b

Question 21

Horizontal vertices hyperbola

Answer 21

(h +/- a, k)

Question 22

Vertical Vertices Hyperbola

Answer 22

(h, k+/- a)

Question 23

Horizontal Co-vertices Hyperbola

Answer 23

(h, k+/- b)

Question 24

Vertical Co-vertices Hyperbola

Answer 24

(h +/- b, k)

Question 25

Horizontal Foci Hyperbola

Answer 25

(h +/- c, k)

Question 26

Vertical Foci Hyperbola

Answer 26

(h, k +/- c)

Question 27

Hyperbola Asymptote Equation

Answer 27

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

Question 28

Hyperbola Pythag. Relation

Answer 28

c²= a²+b²

Question 29

Vertical Equation of a Parabola

Answer 29

(x-h)² = 4p(y-k)

Question 30

Horizontal Equation of a Parabola

Answer 30

(y-k)² = 4p(x-h)

Question 31

Parabola Vertical Focus

Answer 31

(h, k+p)

Question 32

Parabola Horizontal Focus

Answer 32

(h+p, k)

Question 33

Parabola Vertical Directrix

Answer 33

y= k-p

Question 34

Parabola Horizontal Directrix

Answer 34

x= h-p

Question 35

p=

Answer 35

1/4a

Question 36

a=

Answer 36

1/4p

Question 37

Parabola Focal Length

Answer 37

Both: p

Question 38

How to write the equation of a parabola

Answer 38

Determine whether the equation is horizontal or vertical
Plug vertex (h,k) into the correct equation

Question 40

Note: Make sure to find the center

Answer 40

Find the center by finding the letters and see what you can add and subtract to get the numbers in the ordered pairs