Conics Test Flashcards
How to tell if it is a circle
Both are squared and it equals a perfect square
How to graph a circle with the center at (0,0)
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)
How to graph a circle with the center not at (0,0)
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
How to write the equation of a circle
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
Horizontal Major Axis Ellipse Equation
(x-h)² / a² + (y-k)² / b² = 1
Vertical Major Axis Ellipse Equation
(x-h)² / b² + (y-k)² / a² = 1
Major Axis Ellipse
Both: 2a
Minor Axis Ellipse
Both: 2b
Horizontal Vertices Ellipse
(h +/- a, k)
Vertical Vertices Ellipse
(h, k +/- a)
Horizontal Co-vertices Ellipse
(h, k+/- b)
Vertical Co-vertices Ellipse
(h +/- b, k)
Horizontal Foci Ellipse
(h +/- c, k)
Vertical Foci Ellipse
(h, k +/- c)
Pythag. Relation Ellipse
c² = a² - b²
Horizontal Hyperbola Transverse Axis Equation
(x-h)² / a² - (y-k)² / b² =1
Vertical Hyperbola Transverse Axis Equation
(y-k)² / a² - (x-h)² / b² =1
Focal Axis (Line through the Foci)
Both: 2c
Hyperbola Line connecting vertices (transverse axis)
Both: 2a
Line connecting co-vertices (conjugate axis)
Both 2b
Horizontal vertices hyperbola
(h +/- a, k)
Vertical Vertices Hyperbola
(h, k+/- a)
Horizontal Co-vertices Hyperbola
(h, k+/- b)
Vertical Co-vertices Hyperbola
(h +/- b, k)
Horizontal Foci Hyperbola
(h +/- c, k)
Vertical Foci Hyperbola
(h, k +/- c)
Hyperbola Asymptote Equation
Both: y-k = +/- b/a(x-h)
Hyperbola Pythag. Relation
c²= a²+b²
Vertical Equation of a Parabola
(x-h)² = 4p(y-k)
Horizontal Equation of a Parabola
(y-k)² = 4p(x-h)
Parabola Vertical Focus
(h, k+p)
Parabola Horizontal Focus
(h+p, k)
Parabola Vertical Directrix
y= k-p
Parabola Horizontal Directrix
x= h-p
p=
1/4a
a=
1/4p
Parabola Focal Length
Both: p
How to write the equation of a parabola
Determine whether the equation is horizontal or vertical
Plug vertex (h,k) into the correct equation
Note: Make sure to find the center
Find the center by finding the letters and see what you can add and subtract to get the numbers in the ordered pairs
