Conics Art Project
Student Outcomes:
1. Students will be able to apply their understanding of conic sections in a real-world
context by creating an original picture using the conic sections.
2. Students will be able to identify all characteristics of each conic section they created
in their original picture.
3. Students will be able to formulate the appropriate conic equation for each conic section created
in their original picture.
Prompt:
For this task, you will be creating an original piece of artwork using the four conics sections we
learned in this unit as well as lines (circles, ellipses, hyperbolas, parabolas, and lines). Your drawing
will be completed on graph paper. Your original artwork must be school appropriate and must include
the following: (You are encouraged to use other shapes and lines to make the drawing complete that are not
conics.)
o
o
o
o
o
o
o
o
2 circles
2 horizontal or vertical ellipses (or 1 of each)
1 horizontal parabola
1 vertical parabola
1 horizontal or vertical hyperbola
2 lines
At least 1 additional conic shape
Each conic/line should be labeled, include the x and y-axis, and all key graphing
components (vertices, co-vertices,centers, & asypmtotes).
Part 2: Calculate Your Equations (10 pts)

On a separate sheet of paper you must include the following for each conic section/line in your
drawing:
o
o
o
o
o

Circle: radius, center, equation
Ellipse: center, vertices, co-vertices, foci, and equation
Hyperbola: center, vertices, foci, slopes of asymptotes and equation
Parabola: vertex, two points on parabola, focus, directrix, value of “p”, and equation
Line: slope, y-intercept, equation
All equations must be in standard form on an “equation page,” with work shown, written neatly,
clearly labeled, and organized. They should be numbered to correspond with the numbers on the
drawing.
Due Date: _______Thursday, August 27, 2020__BY THE END OF CLASS___
Conic Equations in Standard Form
Line: y = mx + b
Circle: (x – h)2 + (y – k)2 = r2
Horizontal
Vertical
Parabola:
(y – k)2 = ±4p(x – h)
Ellipse:
x  h2   y  k 2
Hyperbola:
a2
b2
x  h2   y  k 2
a2
b2
(x – h)2 = ±4p(y – k)
1
 x  h 2   y  k 2
1
1
 y  k 2  x  h2
1
b2
a2
a2
b2
Sample of a Drawing: YOUR DESIGNS SHOULD BE COLORED!
SAMPLES WILL BE PROVIDED BY THE TEACHER TO GAIN
IDEAS FROM. PLEASE TRY YOUR BEST ON YOUR DESIGN. THIS
IS A TEST GRADE, SO YOU NEED TO GIVE 100%.
PLEASE ATTACH YOUR WORK FOR EACH CONIC TO THE
BACK SIDE OF YOUR DEISIGN. ALSO, PUT YOUR NAME ON
ALL PIECES INCASE THEY GET SEPARATED.
YOU MAY CREATE YOUR PICTURE USING AN ONLINE
SOFTWARE OR YOU MAY DRAW IT BY HAND. ALL WORK
SHOULD BE YOUR OWN AND SHOULD BE COLORED. BE SURE
TO LABEL YOUR AXIS AND EACH SHAPE YOU HAVE
CALCULATED THE EQUATION FOR.