SOLUTION: Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool. I'm not sure where

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool. I'm not sure where       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 195733: Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool.
I'm not sure where to start?
y^2=1-x^2/324 and then square both sides?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2F324+%2B+y%5E2%2F196+=+1+ Start with the given equation.


x%5E2%2F18%5E2+%2B+y%5E2%2F196+=+1+ Rewrite 324 as 18%5E2


x%5E2%2F18%5E2+%2B+y%5E2%2F14%5E2+=+1+ Rewrite 196 as 14%5E2


So the equation is now in the form %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 (which is the general equation of an ellipse) where h=0, k=0, a=18 and b=14


The longest distance between any two points along a line on the ellipse falls on the major axis. The length of the semi major axis simply turns out to be the larger value of "a" or "b"

Since "a" is larger, this means that the length of the semi major axis is 18 units. Double this value to get 36 units.

So the the longest distance across the pool is 36 units.


For the shortest distance, just use the smaller value 14 and double it to 28.


So the the shortest distance across the pool is 28 units.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool.
------------------------
a = sqrt(324) = 18 is one-half the major axis
b = sqrt(196) = 14 is one-half the minor axis
---------------------------
longest distance = 2*18 = 36
---
shortest distance = 2*14 = 28
---
Cheers,
Stan H.