The California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
16. Students demonstrate and explain
how the geometry of the graph of a
conic section (e.g., asymptotes, foci,
eccentricity) depends on the
coefficients of the quadratic equation
representing it.
Skills (Note: none listed for science standards)
Teacher Strategy
Have transparencies showing a plane through
the hollow double cone forming a parabola,
circle,and ellipse for a hyperbola.The teacher
can show students how the intersection of the
plane and a double cone form a circle.Have
students demonstrate the circle,ellipse or
hyperbola.Repeat the same steps for ellipses when the
major axis is on the X and Y axis.
Student Tasks or Scientific Investigation/Experimentation
Have students set up a polynomial equation of a
set of points.Where the distance from a fixed
point (F,O)is e times its distance from the vertical
line x =–f where e stands for a constant.Have
students show the graph is an ellipse if 0 <e <1,
a parabola if e =1,and a hyperbola if e >1.
Assessment or Scientific Application/Assessment
Have students solve various quadratic equations
to prove what type of conic section it is.Have
students determine the eccentricity for a circle
and determine its directrix.
Resources and Technology
Resource:“Fireworks ” unit from the third year
textbook of the Interactive Mathematics
Program ™ ((IMP ™)deals with parabolas.
Contact Key Curriculum Press at 1-800-995-
MATH for ordering information.Resource:Advanced Geometric Constructions
by Alfred Posamentier and William Wernick,
Dale Seymour Publications.Technology:Have students investigate how ships
at sea in the LORAN system (for Long Range
Navigation)find their location by receiving
radio signals which locate them on several
hyperbolas.
This page is taken from the Santa Clara Office of Education.