580 Words3 Pages

Name: Carla Strombitski | Date: |
Graded Assignment
Unit Test, Part 2: Conic Sections
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.
(10 points) Score | |
1. The equation of an ellipse is given by .
a. Identify the coordinates of the centre of the ellipse.
b. Find the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. Label the center and foci.
Answer:
a) Given equation of ellipse. On comparing this equation with standard equation of ellipse with centre (h,k) which is given by x-h2a2+y-k2b2=1 , we have ,
h = 3 and k = -5.
Therefore, coordinates of centre of ellipse = (3, -5).
b) Given equation of ellipse. On comparing this equation with standard equation of ellipse with major axis 2a and minor axis 2b which is given by x-h2a2+y-k2b2=1 , we have,
a2=64=>a=8
And b2=100=>b=10
Therefore, length of major axis = 2a = 2*8 = 16.
And length of minor axis = 2b = 2*10 = 20.
c) From part a) and b), we have a = 8 and b = 10 and h=3,k=-5
So, c2=b2-a2=102-82=100-64=36
=>c=sqrt36= 6.
In this given equation b>a
So, this is a vertical ellipse.
Therefore, coordinates of foci = (3, -5+6) and (3, -5-6)
Foci are (3,1) and (3, -11).
d)
This is the graph of given ellipse with foci and center.
(12 points) Score | |
2. The equation of a hyperbola is given by .
a. Identify the coordinates of the center of the hyperbola.
b. Find the length of the transverse and conjugate axes.
c. Find the slopes of the asymptotes.
d. Find the coordinates of the foci.
e. Graph the hyperbola. Label the center, midpoints of the associated rectangle, and foci.
Answer:
a) Given equation of hyperbola
On comparing this equation with standard equation of hyperbola with centre (h,k) which

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