anonymous
  • anonymous
HELP PLEASE!!!! find the equation of ellipse. center @origin. Passing through (2, square root 30 / 3.), distance between directrices 24 square root 7 / 7.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{ x^{2} }{ a^{2} }+\frac{ y ^{2} }{ b^{2}}=1\] can you identify this equation?
anonymous
  • anonymous
yes its ellipse
anonymous
  • anonymous
so plug in the values of (x,y) i.e \[(2,\sqrt{30}/3)\] in that equation

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anonymous
  • anonymous
okayy..
anonymous
  • anonymous
now dist. of directrix from origin is a/e where e^2=1-(b/a)^2
anonymous
  • anonymous
so dist between 2 directrices will be 2a/e
anonymous
  • anonymous
yes and eccentricity not given...
anonymous
  • anonymous
so we find eccentricity in terms of a^2 and b^2
anonymous
  • anonymous
how do we get a? b?
anonymous
  • anonymous
okay let's visualize the problem first
anonymous
  • anonymous
you want the equation right?
anonymous
  • anonymous
so you want a, b
anonymous
  • anonymous
yes yes
anonymous
  • anonymous
so first lets use the co-ordinates given and plug it in the master eqn of ellipse
anonymous
  • anonymous
so you get a eqn with 2 unknown i.e a,b
anonymous
  • anonymous
you need 1 more to find the exact values for a,b
anonymous
  • anonymous
for that 2a/e = dist between directrices
anonymous
  • anonymous
2 coordinates?
anonymous
  • anonymous
itz co-ordinate not plural ..sorry
anonymous
  • anonymous
typo..
anonymous
  • anonymous
co-ordinate is (2, sqrt30/3) use it in ellipse eqn
anonymous
  • anonymous
eqn will be 4/a^2 +10/b^2 =1
anonymous
  • anonymous
yeah. thats what i did
anonymous
  • anonymous
now you answer me what's 2a/e?
anonymous
  • anonymous
distance between directrix and i dont know how to get e
anonymous
  • anonymous
|dw:1378823593019:dw|
anonymous
  • anonymous
\[e ^{2}=1-\ \frac{ b ^{2} }{ a ^{2}}\]
anonymous
  • anonymous
therefore plug in this eqn to find dist .. i.e \[4a ^{2}/e ^{2}=dist ^{2}\]
anonymous
  • anonymous
where dist =
anonymous
  • anonymous
24 sqrt 7/7
anonymous
  • anonymous
4a^2 / e^2.. how did you come up with this??
anonymous
  • anonymous
look at the graph directix lies at a/e.. therefore dist between both of them is 2a/e
anonymous
  • anonymous
got it?
anonymous
  • anonymous
yey!
anonymous
  • anonymous
yippie!!
anonymous
  • anonymous
and.. how about getiing e?
anonymous
  • anonymous
anything else?
anonymous
  • anonymous
i already ut the dist on the equation and what's next?
anonymous
  • anonymous
already put the distance on the equation
anonymous
  • anonymous
e defined like that.. and for ellipse its the eqn written above ingeneral e=distance of locus of point from focus/ perpendicular dist. of locus point from directrix
anonymous
  • anonymous
now you get a eqn in a^2 and b^2 again
anonymous
  • anonymous
right??
anonymous
  • anonymous
yes..
anonymous
  • anonymous
so you can now solve for 2 linear eqn with 2 variable .. right..?? note that you need to find a^2 and b^2 not a, b.. so i used the term linear eqn as you can put a^2=p and b^2=q
anonymous
  • anonymous
still confused?
anonymous
  • anonymous
yes..
anonymous
  • anonymous
at which part?
anonymous
  • anonymous
the e part.. dont know how to solve. what i know is the first equation would be the 4/a^2 +10/b^2 =1 and yeah stuck up no idea about the secodn equation..
anonymous
  • anonymous
suppose u have a eqn ... 2a/e=24 sqrt7/7
anonymous
  • anonymous
now u have a eqn of e in terms of a^2,b^2.. (the eqn just below the graph i drew)
anonymous
  • anonymous
now substitute this eqn of e in the dist eqn above..
anonymous
  • anonymous
square both sides.. u'll get eqn. in a^2 and b^2
anonymous
  • anonymous
and..
anonymous
  • anonymous
so now substitute a^2 by p and b^2 by q in both the obtained .. u get eqn in p,q .. now from one eqn find p in terms of q .. then substitute this in the second equation

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