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