2009

STRAIGHT

Calculate the slope m and the general equation of the line through the points given respectively by then. Plot and conclude the case with the graph as that change m (Class of Line).

1. A : (3, 2) and B : (5, -4)

2. A : (4, -1) and B: (-6, -3)

3. A : (2.5) and B : - (7, 5)

4 . A : (5,-1) y B : (-5, 6)

5 . A : (-3, 2) y B : (-3, 5)

6 . A : (4,-2) y B : (-3,-2)

7 . A : (6,-7) y B : (1, 9)

8 . A : (2,7) y B : (-5, 8)

9 . A : (12,-3) y B : (6,-5)

10 . A : (4, -5) and B: (-3, 6).

Draw the line through P , for each value of m .

11. P : (-3.1) m ½, 1 / 5, -3

12 . P : (-2, 4); m -1, -2, -1 / 2

13 . Given the line: kx - and = + 3 k, determine a value of k to point P ( -3, 7) belongs to this line.

Get in general the equation of the line through point A and satisfies the given condition.

14. A : (2, -1) and its slope is -1 / 2

15. A : (-1, 9) and its slope is 3 / 4

16. A : (-3, 5), parallel to the line x + 3 = and - 1.

17. A : (7, -3), perpendicular to the line 2 x and + 5 = 8.

18. A : (5, -2) perpendicular to the axis and .

19. A : (-4, 2) parallel to the x .

20. A : (-1, 4); pending 2 / 3

Calculate the slope m and the equation of the line through the points given respectively by then. Plot and conclude the case with the graph as m changes.

21. A: (2.5) and B: (-7, 5)

22. A: (-3, 2) and B: (-3, 5)

23. Get in general the linear equation passing through point A and satisfies the given condition.

A: (-7, -3), perpendicular to the line 2x - 5y = 8.

24 and 35 QUESTIONS ARE MULTIPLE CHOICE ANSWER ONLY

24. The equation of the straight line through the point (-3.0) and is parallel to the line Y - X = 3 is:

A. X - Y + 3 = 0

B. X + Y + 3 = 0

C. - X + Y + 3 = 0

D. X - Y - 3 = 0

25. The equation of the straight line through the point (-3, -2) and perpendicular to the line X + Y = 3 is:

A. X - Y + 1 = 0

B. X + Y + 1 = 0

C. - X + Y + 1 = 0

D. X - Y - 1 = 0

circumference

WRITE
NORMAL FORM OF THE EQUATION the circle through the points with the coordinates given. THEN IDENTIFIES THE CENTER OF THE CIRCLE AND THE RADIO.

(7, -1), (11, -5), (3, -5)

(1.3), (5.5), (5.3 )

(5.3), (-2,2), (-1, -5)

(-10, -5), (-2.7), (- 9.0)

(1.3), (5.5) (5.3)

(7, -1), (7.5), (1, -1)

(2, -1), (-3.0) (1.4)

WRITE THE EQUATION OF CIRCUMFERENCE TO MEET EACH SET OF CONDITIONS .

The circle through (7, -1) and is centered at (-2.4)

The circle through the origin and has its center at (-3,4)

diameter ends are the points (-2, -3) and (4.5)

The ends of a diameter are the points (-3,4) and (2.1)

GRAPHIC

(x-4) 2 + (y -1) ² = 25

(x +3) 2 + (y +5) = 16 ²

² 4x +4 y = 49 ²

(x +3) 2 + (y +5) = 16 ²

^{x 2 + 14x +} and 2 + 6y + 50 = 0

Think critically. Find the radius and the coordinates of the center of the circle defined by the equation x + y ² 2 - 2x + 4y + 5 = 0. Describe the graph.

Write the equation of the family of circles in which h = k and the radius is 8. Make k is any real number.

If the equation of the circle is written in canonical form 2 h + k-r ² 2 = 0. What can you say about the graph of the equation?

ELLIPSE

1) Find the general equation of the ellipse with center at the origin, focus (0, 3) and its semi-major axis is 10 units.

2) Find the equation of the ellipse with center at the origin, a vertex (0.8) and a focus on (0, -2)

3) Obtain the equation of the ellipse whose vertices are located at (-5, 9) and (-5, 1) and the length of the straight side is 3 units.

4) Find the equation of the ellipse with center at C (3, 1), a vertex is the point (3, - 2) and the length of the straight side is equal to 16 / 3

5) Given the equation 3x + 4y ² 2 = 12, find the coordinates of its elements.

6) For each of the following equations representing ellipses, also calls for certain drawing vertices and hotspots:

a. ^{16x 2 + 25y} ^{2 = 100}

b. 9x 2 + 4y = 36 ²

c. 2 4x + y = 16 ²

d. x ² ^{2 + 9y = 18}

e. + 4y 2 x 2 = 8

f. ^{4x 2 + 9y} ^{2 = 36}

7) In the following exercises find the equation of the ellipse that satisfies the given conditions. Trace your graphic.

· Center at (0, 0); focus on (3, 0), vertex (5, 0).

· Center at (0, 0); focus on (-1, 0), vertex (3, 0).

· Center at (0, 0); focus on (0, 1), vertex (0, -2).

· Focuses on (± 2, 0), length of major axis 6.

· Focuses on (0, ± 3), the intersections with the x-axis are ± 2.

· Center at (0, 0), vertex (0, 4), b = 1.

· vertices at (± 5, 0), c = 2.

· Center (2, -2), vertex (7, -2); foci (4, -2).

· Focuses on (5, 1) and (-1, 1), length of major axis is 8.

· Center (1, 2), focuses on (1, 4), passes through the point (2, 2).

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