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Mathematics 19 Online
OpenStudy (allieeslabae):

help?

OpenStudy (allieeslabae):

OpenStudy (johnweldon1993):

Alright so we have the standard form \[\large \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\] Meaning we have \[\large \frac{x^2}{2500} + \frac{y^2}{8100} = 1\] Making a = 50 and b = 90 right?

OpenStudy (johnweldon1993):

.....patiently awaiting your answer >:P

OpenStudy (allieeslabae):

Okay..?

OpenStudy (johnweldon1993):

Actually I should ask right away...how would you go about this problem?

OpenStudy (allieeslabae):

Wait john what do you mean?

OpenStudy (allieeslabae):

we're trying to find the length of the track.

OpenStudy (johnweldon1993):

Just the length of the major axis of the track :)

OpenStudy (allieeslabae):

Ohh okay... but whats the next step...

OpenStudy (allieeslabae):

90^2 was the 1800??? no.

OpenStudy (allieeslabae):

*8100

OpenStudy (allieeslabae):

So now we're looking for h and k.

OpenStudy (johnweldon1993):

Okay well the FIRST step would have been to say I was WRONG! I said a = 50 and b = 90 BUTTTTT we should know a is the larger of the 2 denominators \[\large \frac{x^2}{50^2} + \frac{y^2}{90^2} = 1\] *And yes 50^2 = 2500 and 90^2 = 8100* This would give a = 90 and b = 50 *since A is always the bigger of the two

OpenStudy (johnweldon1993):

And oh god no...much easier than that!

OpenStudy (allieeslabae):

Wait you lost me...

OpenStudy (johnweldon1993):

Okay okay...dont look at anything above this point!

OpenStudy (allieeslabae):

I thought before a was 50 now its 90

OpenStudy (allieeslabae):

lol

OpenStudy (johnweldon1993):

We have the standard form of an ellipse \[\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] \[\large \frac{x^2}{2500} + \frac{y^2}{8100} =1\] One thing to know *I was testing you earlier!* is that 'a^2' is always the larger of the 2 denominators! Meaning here we would have a^2 is ACTUALLY 8100 or a = 90 And b^2 is ACTUALLY 2500 or b = 50

OpenStudy (johnweldon1993):

From here, it is simply \(\large \text{Major Axis Length} = 2a\)

OpenStudy (allieeslabae):

okay... how about this problem. We're not getting anywhere with you TESTING me.. bwahahha

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