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LEARNING ACTIVITY SHEET
PRE-CALCULUS
Quarter 1 Week 4
Name: ________________________________ Score: _______________ Grade & Section: ______________________ Date: ________________
Investigating Hyperbolas
I. Learning Competency
Define a hyperbola (STEM_PC11AG-Id-1) Determine the standard form of equation of a hyperbola (STEM_PC11AG- Id-2)
II. Objectives
The learner must be able to define hyperbola and determine the standard form of equation of a hyperbola
III. Activities
Activity 1
A. Sketch the graph of the given equation. Show its center, vertices and foci.
B. Find an equation of the hyperbola with the given conditions.
- has vertices at and foci at.
GUIDE QUESTIONS: a. What is the center of the hyperbola? b. If the vertices are at what is the value of a? c. If the foci are at what is the value of c? d. Can you get b given a and c? What is the length of b?
- having center at a focus at , and a vertex at
GUIDE QUESTIONS: a. From the center and the given focus, what is the value of c? b. From the center and the given vertex, what is the value of a? c. Can you get b given a and c? What is the length of b?
- whose center is at ; vertices at and ; and endpoints of conjugate axis at and.
GUIDE QUESTIONS: a. What is the center of the hyperbola? b. From the center and the given vertices, what is the value of a? c. Given the endpoints of the conjugate axis, what is the value of b?
Activity 2 Graphs and Equations of Hyperbolas
A. Sketch the graph of each equation. Show its center, vertices and foci.
B. Find the standard equation of the hyperbola with the given conditions.
- centered at the origin and whose foci are at and vertices at
.
- with vertices at (0, 2) and (4, 2) and foci at (−1, 2) and (5, 2).
- with center at vertices at and endpoints of
conjugate axis at.
Activity 4 Coloring Hyperbola
https://www.bestcoloringpagesforkids.com/free-printable-color-number-coloring-pages.html
Activity 5 HYPERBOLAS Summative Assessment
Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.
- What refers to the set of all points in a plane such that the difference of the distances from to two fixed points is a given constant? a. Circle c. Ellipse b. Parabola d. Hyperbola
- Which of the following equations illustrates a hyperbola centered at the origin? a. c. (^8) b. d. (^8)
- Which of the following equations illustrates a hyperbola centered at (h,k)? a.. c.
b. d. (^8)
- What is the center of the hyperbola with an equation ? a. c. b. d.
- What is the value of a the equation? a. b. c. d.
- What is the value of c in the equation? a. b. c. d.
- What is the standard equation of the hyperbola centered at the origin with foci at and vertices at? a. c. b. d.
- What is the standard equation of the hyperbola having (-5,1) and (3,1) as the endpoints of its conjugate axis and has vertices at (-1,4) and (- 1,-2)? a. c. b. d.
