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 panoptic credit.
(10 points)
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1.       The par of an ellipse is assumption by .
a. Identify the coordinates of the centre of the ellipse.
b. befall the length of the major and minor axes.
c. Find the coordinates of the foci.
d. Graph the ellipse. pass judgment the center and foci.
Answer:
a) wedded par of ellipse.
On analyse this equation with standard equation of ellipse with centre (h,k) which is abandoned 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 equivalence this equation with standard equation of ellipse with major bloc 2a and minor axis vertebra 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.
Â
(12 points)
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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 coupled 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:
Â
a) Given equation of hyperbola
On comparing this equation with standard equation of hyperbola with centre (h,k) which is given by y-k2b2-x-h2a2=1 , we have,
h=6 and k=0
Therefore, coordinates of center of...If you want to get a full essay, order it on our website: Ordercustompaper.com
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