If you use the zeros, you can write the factored form of p (x) as p (x) = (x + 3/4) (x - 4/3) * (x - 2/5) than as p (x) = (4x + 3) (3x - 4) * (5x - 2). What is the relationship of the factors between two forms? Give this relationship in general form.

Answer: The standard form for the equation of an ellipse is:

(

x

-

h

)

2

a

2

+

(

y

-

k

)

2

b

2

=

1

The center is:

(

h

,

k

)

The vertices on the major axis are:

(

h

-

a

,

k

)

and

(

h

+

a

,

k

)

The vertices on the minor axis are:

(

h

,

k

-

b

)

and

(

h

,

k

+

b

)

The foci are:

(

h

-

√

a

2

-

b

2

,

k

)

and

(

h

+

√

a

2

-

b

2

,

k

)

To put the given equation in standard form, change the + 2 to - - 2 and write the denominators as squares:

(

x

-

3

)

2

4

2

+

(

y

-

-

2

)

2

3

2

=

1

The center is:

(

3

,

-

2

)

The vertices on the major axis are:

(

-

1

,

-

2

)

and

(

7

,

-

2

)

The vertices on the minor axis are:

(

3

,

-

5

)

and

(

3

,

1

)

Evaluate:

√

a

2

-

b

2

=

√

4

2

-

3

2

=

√

16

-

9

=

√

5

The foci are:

(

3

-

√

5

,

-

2

)

and

(

3

+

√

5

,

-

2

)