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parabola help = =" (1 Viewer)
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pLuvia
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Post questions up and I'm sure people will help you.
Look through your textbooks, read the examples
Look through your textbooks, read the examples
Wackedupwacko
Member
basically its writing the caretesian equation (eg x² = 4ay) in a form where y = ? and x =? that will satisfy your cartesian equation. to turn it back all you hafta do is spot say the same variable in it eg x= 2at y=at² , make t the subject in the first one so u get
t= x/2a , sub into 2nd one and u get y= ax²/4a² , which is x² = 4ay
there are other forms but basically all you do is look to eliminate the variable that wont be used and maintaining your x and y...
another example is circle x = rcos@ and y= rsin@ : so you ask yourself how do u eliminate the cos and sin (as they obviously wont be in the cartesian form) well simple by adding the squares thus
x² = r²cos²@ and y²=r²sin²@ , add them together and u have:
x² + y² = r²(cos²@ + sin²@) <---- = 1 thus u have your basic circle
t= x/2a , sub into 2nd one and u get y= ax²/4a² , which is x² = 4ay
there are other forms but basically all you do is look to eliminate the variable that wont be used and maintaining your x and y...
another example is circle x = rcos@ and y= rsin@ : so you ask yourself how do u eliminate the cos and sin (as they obviously wont be in the cartesian form) well simple by adding the squares thus
x² = r²cos²@ and y²=r²sin²@ , add them together and u have:
x² + y² = r²(cos²@ + sin²@) <---- = 1 thus u have your basic circle
One of the hardest bits of parametrics is finding the locus. To find locus:
1. Find the general point of the locus, this will always be expressed in terms of a few variables, usually a, and 1 or 2 parameters, like p and q
2. Since this point is variable we let the co-ordinates be equations x=#$@#$ and y=@#$@#@$ where @#$@#% is some random expression, lol.
3. The locus will always be found by simultaneously solving the two equations, and will nearly always involve eliminating all the parameters, ending up with a cartesian equation (with only x, y and frequently a). This will be your locus. To eliminate the parameters, use a restriction on the parameters, e.g pq=-1 or p+q=2. This restriction will nearly always be asked to show earlier on in the question.
Finding the locus questions are nearly always at the end of a Q, and the Q will usually take you through everything like showing this and that, and finding a restriction, finally finding the locus.
1. Find the general point of the locus, this will always be expressed in terms of a few variables, usually a, and 1 or 2 parameters, like p and q
2. Since this point is variable we let the co-ordinates be equations x=#$@#$ and y=@#$@#@$ where @#$@#% is some random expression, lol.
3. The locus will always be found by simultaneously solving the two equations, and will nearly always involve eliminating all the parameters, ending up with a cartesian equation (with only x, y and frequently a). This will be your locus. To eliminate the parameters, use a restriction on the parameters, e.g pq=-1 or p+q=2. This restriction will nearly always be asked to show earlier on in the question.
Finding the locus questions are nearly always at the end of a Q, and the Q will usually take you through everything like showing this and that, and finding a restriction, finally finding the locus.