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Some problems with conic sections

  • Thread starter Mspike6
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  • #1
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Here are some conic questions that am having problems with :

1) The general form of a particular ellipse is show Below. If the conic is translated 2 units left and 1 unit down, determine the new general term.

2x2+y2-2x+3y-9=0
Solution,
i figureed that we will have to convert this to Sandard form so we can apply the Trans;ations.

2x2-2x y2-3y=0

Then we need to complete the squares

2(x2-x+[tex]\frac{1}{4}[/tex]) + (y2-3y+[tex]\frac{9}{4}[/tex])=9+1/2+9/4

When i divided the whole thing by 11.75 so i can get 1 on the Right hand side, a fractions come up on the right hand side, and i just can't get it to the Standard form of the elipse

2) Find the equation of a hyperbola in standard form or general form, that has its centre at (-2, 5), one vertex at (-2, 10), and the slope of one of its asymptotes is 5/4 .

Solution:
I drew the Hyperbola so i can imagine it, and i guessed that a = 5 since the center point is at (-2,5) and the Vertex is at (-2,10)

The slops are b/a and -b/a
So it should be b/5 not b/4

aint what am saying right ?
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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The standard equation of ellipse becomes
(x - 1/2)^2/(47/8) + (y-3/2)^2/(47/4) = 1
 
  • #3


Whats the question?
 
  • #4
63
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Sorry, i meant to ask if what i did is correct , or is there something am missing ?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,792
919


Here are some conic questions that am having problems with :

1) The general form of a particular ellipse is show Below. If the conic is translated 2 units left and 1 unit down, determine the new general term.

2x2+y2-2x+3y-9=0
There is no need to convert to standard form. "Translating 2 units left" is exactly the same as adding 2 to x. "Translating one unit down" is exactly the same as subtracting 1 from y. Replace x by x+2 and y by y- 1.


2) Find the equation of a hyperbola in standard form or general form, that has its centre at (-2, 5), one vertex at (-2, 10), and the slope of one of its asymptotes is 5/4 .
Rotating through an angle [itex]\theta[/itex] gives [itex]x'= x cos(\theta)+ y sin(\theta)[/itex], [itex]y'= x sin(\theta)- y cos(\theta)[/itex]. Replace x by [itex]x cos(\theta)+ y sin(\theta)[/itex], y by [itex]x sin(\theta)- y cos(\theta)[/itex]. [itex]\theta= arctan(5/4)[/itex].
 
  • #6
63
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There is no need to convert to standard form. "Translating 2 units left" is exactly the same as adding 2 to x. "Translating one unit down" is exactly the same as subtracting 1 from y. Replace x by x+2 and y by y- 1.



Rotating through an angle [itex]\theta[/itex] gives [itex]x'= x cos(\theta)+ y sin(\theta)[/itex], [itex]y'= x sin(\theta)- y cos(\theta)[/itex]. Replace x by [itex]x cos(\theta)+ y sin(\theta)[/itex], y by [itex]x sin(\theta)- y cos(\theta)[/itex]. [itex]\theta= arctan(5/4)[/itex].
Thanks alot ! :D
really appreciate it
 

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