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).
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.
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
A. X - Y + 3 = 0
B. X + Y + 3 = 0
C. - X + Y + 3 = 0
D. X - Y - 3 = 0
A. X - Y + 1 = 0
B. X + Y + 1 = 0
C. - X + Y + 1 = 0
D. X - Y - 1 = 0
WRITE
- (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)
- 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)
- (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?
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).