Honors Advanced Math Name:________________________________ Conic Section Review Problems Direction

Honors Advanced Math Name:________________________________ Conic Section Review Problems Directions: Here are some extra problems on conic sections. Some are problem types that we've already done and some are a little new.

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Honors Advanced Math Name:________________________________
Conic Section Review Problems
Directions: Here are some extra problems on conic sections. Some are problem types that we've already
done and some are a little new. All of them are within your reach. In studying for your test, you should
also make sure you understand the problems from the previous homework assignments and that you know
how to do all of the major proofs from the unit.
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1. Consider the relation 36x +72x +9y +6y-z -4z =114.
a. Put this equation into its usual form and describe it. What type of relation is this? (An ellipsoid,
some type of hyperboloid, etc). You may wish to include a sketch as part of your answer, but you
are not required to do this.
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b. List a sequence of graphical transformations that would turn the graph of x + y -z =1 into the
graph of the above relation.
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c. Sketch the cross section in the plane y =- . Include the coordinates of all major points (center,
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vertices, foci) and any asymptotes (with equations for the asymptotes).
d. Sketch the cross section in the plane x = -1. Include the coordinates of all major points (center,
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vertices, foci) and any asymptotes (with equations for the asymptotes).
2. Find the coordinates of the point(s) where the line x,y,z = 7,-3,2 + t 4,2,2 intersects the ellipsoid
( ) ( )
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2
( )
x-3 z
2
+(y +5) + =1. Hint: Think back to a few units ago and remember that we've done the
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problem of a line intersecting a sphere. The same procedure will work for this problem.
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2
( ) (y +7)
x +3
3. Consider the equation - =1.
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a. Sketch the graph without using your calculator. Include the coordinates of all major points (center,
vertices, foci) and any asymptotes (with equations for the asymptotes).
b. Asymptotes can be useful for estimating the coordinates of points on a curve. Use the asymptotes
that you got in part a to estimate the values of y when x = 347. Then check your...