HONORS ALGEBRA 2
CONICS
10-1 Exploring Conic Sections
We are going to use an interactive graphing calculator called Desmos to explore the
conic sections. Geometrically, the conic sections are the four types of plane sections you
can get by cutting two con
10-2 Circles
Algebra 2H
Circle
Tangent
Reminder:
The 2-D midpoint formula: _
The 2-D distance formula: _
(x,y)
The distance formula can be used to find a
general equation for a circle with center (h, k)
and radius r:
General Equation of a Circle:
_
Ex 1:
10-3 Ellipses
Algebra 2H
Ellipse
focus of an ellipse
major axis
vertices of an ellipse
minor axis
co-vertices of an ellipse
Formal definition of an ellipse: the set of points P (x, y)
in a plane such that the sum of the distances from any
point P on the e
Ex1: Identify theconicsection,checkingtomakesureitsnotdegenerate.Make
sure you start with your equation in standard form!
A) 4x2-10xy+5y2+12x+20y=0
B) 9x2-12xy+4y2+6x=8y
C) 4x2 +16x+16=0
D) 9x2+ 9y2-18x-12y-50=0
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Chapter 10 Notes
Ellipse and Hyperbolas
10-3 and 10-4
name_
Do all work on separate paper. There is not enough room here to show what you need to show : )
-Find the constant sum/difference of an ellipse/hyperbola with the given foci and point on the figure.
1
F 1 (40, 0),
FORMULA SHEET CH. 10
Algebra 2H
You may use this on tests and quizzes
CIRCLES:
Equation
(
)
(
)
ELLIPSE:
Major Axis Horizontal
Equation
( x h) 2 ( y k ) 2
1, a>b
a2
b2
c 2 = a 2- b 2
Vertical
( x h) 2 ( y k ) 2
1, a>b
b2
a2
d=PF1+PF2
HYPERBOLA:
Transver
Worksheet 10-6
Algebra 2H
Identify the conic section that equation represents, checking to see if its
degenerate. Show all work for credit.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
10-5 Parabolas (in terms of distance)
Algebra 2H
vertex of a parabola
axis of symmetry
focus, F
directrix
parameter
parabola - set of all points, P(x, y), in a plane that are and equal distance from
both a fixed point, called the focus, and a fixed line,
Ex 1: What kind of conics are the following?
a)
c)
b) (x 1) 2 + (y 1) 2 = 1
d)
You can use your graphing calculator to see the conics BUT you have to solve
for y first. If the conic itself is not a function, you can split it into a piecewise
function to v
10-4 Hyperbolas
Algebra 2H
Hyperbola
focus of a hyperbola
branch of a hyperbola
transverse axis
vertices of a hyperbola
conjugate axis
co-vertices of a hyperbola
Formal definition of a hyperbola: the set of points P(x, y) in a plane such that the
differen