8.2.4 (033-T2-16 $8.2)

a) I

b) I and II

c) I, II, III and IV

d) I and IV

e) II and III

Solution:

The fact that x is equal to the square root of something ==> x must be positive.

The fact that y is under the square root ==> that y must be positive.

Therefore, the intersection will be in the Quadrant I only.

To find the point of intersection:

==>

Square both sides

==>

Substitute in the second equation

==>

Solution:

Form of the ellipse read from the given foci

Midpoint formula

Center:

and

==>

==>

==>

Therefore, the equation of the ellipse is:

==>

Find b in terms of a using the given slope.

Substitute the center and b.

Substitute the given point.

==>

==>

==>

Solve

for a

==>

Vertices:

and

==>

or

==>

==>

or

Section 8.3

8.3.1 (033-T2-18 $8.3)

Solution:

Form of the hyperbola. Transverse axis parallel to the x-axis ==> x term is positive.

Solution:

This is the graph of the right half of a standard ellipse.

Eqn of the ellipse

==>

Solve for x to find the eqns of the right and left sides of the ellipse.

Thus,

Eqn of the right half.

or

Eqn of the left half

8.1.3 (033-T2-14 $8.1)

Math 002

Solution of Old Exam Problems

Chapter 8

A. M. Farhat

Section 8.1

8.1.1

Find the vertex, focus and the directrix of the parabola .

Solution:

Rewrite the eqn. in the standard form

==>

Therefore,

Vertex:

Focus:

Directrix:

Graph of the parabola.

8.1.2

Find the equation represented by the graph shown below.

Foci:

and

==>

8.2.2 (033-T2-10 $8.2)

a) -2

b) 1

c) -3

d) 2

e) 3

8.2.3 (033-T2-11 $8.2)

8.1.4 (033-T2-15 $8.1)

Section 8.2

8.2.1 (033-T2-9 $8.2)

a) 2

b)

c) 3

d)

e)

Solution:

Complete the squares

Center: