Allowed Formulas
Conic Sections are curves that result from the
intersection of a cone and a plane.
PARTS OF A PARABOLA
7.2 – The Parabola
7.2 – The Parabola
Find the vertex, focus, and the directrix of the following parabola.
Graph the equation.
2 14 8 25y y x+ = −
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
PARTS OF AN ELLIPSE
major axisminor axis
The major axis is in the direction of the longest part of the ellipse
7.3 – The Ellipse
center focifoci
The vertices are at the ends of the major axis
7.3 – The Ellipse
Analyze the equation; that is, find the center, foci, and vertices of the
ellipse. Graph the equation.
( ) ( )2 2
1 41
25 9
x y− ++ =
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
7.3 – The Ellipse
Find an equation for the ellipse described. Graph the equation.
Foci at (0,3) and (-4,3); vertex at (-6,3)
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
7.3 – The EllipseFall 2008 Final Exam
7.3 – The Ellipse
Analyze the equation. Find the center, foci,
vertices, and graph the equation.2 24 3 8 6 5x y x y+ + − =
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−1
1
2
3
4
5
6
7
8
9
x
y
−10
−9
−8
−7
−6
−5
−4
−3
−2
PARTS OF A HYPERBOLA
co
nju
gate
axis
The black dashes lines are asymptotes for the graphs.
transverse axis
7.4 – The Hyperbola
centerfocifoci
co
nju
gate
axis
transverse axis
7.4 – The Hyperbola
Find the equation of the hyperbola whose graph is given below.
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−3
−2
−1
1
2
3
4
5
6
7
8
9
x
y
−10
−9
−8
−7
−6
−5
−4
7.4 – The Hyperbola
Analyze the equation; that is, find the center, foci, and vertices of the
hyperbola. Graph the equation and include the asymptotes on your
sketch.
( ) ( )2 2
2 31
16 4
x y+ −− =
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
7.4 – The HyperbolaFall 2008 Final Exam