Question 195733
{{{x^2/324 + y^2/196 = 1 }}} Start with the given equation.



{{{x^2/18^2 + y^2/196 = 1 }}} Rewrite {{{324}}} as {{{18^2}}}



{{{x^2/18^2 + y^2/14^2 = 1 }}} Rewrite {{{196}}} as {{{14^2}}}



So the equation is now in the form {{{(x-h)^2/a^2+(y-k)^2/b^2=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.