Question

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 1

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

)