anonymous
  • anonymous
The orbit of the planet Pluto is and ellipse with the sun at one focus. The maximum distance between the sun and Pluto is 7,375 km, and the minimum distance is is 4,425 km. How far (in millions of km) is it across Pluto's orbit at its widest point? a) 5,900 b) 11,425 c) 11,800 d) 5,712.65
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what do u mean by the widest point?
anonymous
  • anonymous
I guess Pluto's furthest orbit form the sun. I'm not 100% sure, that's all the question says.
anonymous
  • anonymous
if u draw an ellipse then the point of maximum distance from one of the focus would be the farthest point on orbit

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anonymous
  • anonymous
A little confusing. How would this be done?
anonymous
  • anonymous
i can help u find out the equation of the elliptical path though
anonymous
  • anonymous
Okay, how?
anonymous
  • anonymous
let it be \[{x ^{2}/a ^{2}} + y ^{2}/b ^{2} =1\] b^2=a^2(1-e^2) e is ur coeff of eccentricity foci are at (ae,0) and (-ae,0) see a general diagram of ellipse a+ae=maximum distance from focus=7375 a-ae=min dist from focus=4425 find a , e
anonymous
  • anonymous
do you have a general equation, with conics
anonymous
  • anonymous
yes
anonymous
  • anonymous
even for a hyperbolic path
anonymous
  • anonymous
yes whats your equation with that e thingy , thats cool, for any conic
anonymous
  • anonymous
Does anybody know the answer? I'm not doing so well with the equation..
anonymous
  • anonymous
e is called ur coefficient of eccentricity that equation is only for an elliptical path
anonymous
  • anonymous
This is an elliptical path though. What is the foci?
anonymous
  • anonymous
(-ae,0) and (ae,0)
anonymous
  • anonymous
I mean what does it represent? Like a definition.
anonymous
  • anonymous
foci are the two points on the major axis of the ellipse An ellipse can be drawn using two drawing pins, a length of string, and a pencil: Push the pins into the paper at two points, which will become the ellipse's FOCI. Tie the string into a loose loop around the two pins. Pull the loop taut with the pen's tip, so as to form a triangle. Move the pen around, while keeping the string taut, and its tip will trace out an ellipse.
anonymous
  • anonymous
That's a very interesting way to draw an ellipse, never heard of that technique, Thank you. Now in solving this problem, what do I need to plug into your equation to come up with numbers?
anonymous
  • anonymous
try to visualize it sun is at (-ae,0) one of the foci max distance would be when pluto is at (a,0) so, a+ae=7375 work out for min distance in the same way
anonymous
  • anonymous
Would it be either -a+ae=4,425 or a-ae=4,425?
anonymous
  • anonymous
a-ae would give the correct answer
anonymous
  • anonymous
Does a=2,950?
anonymous
  • anonymous
or no, ae?
anonymous
  • anonymous
ae would be 1475 a = 5950
anonymous
  • anonymous
Does e=0.248?
anonymous
  • anonymous
I got C. Is that correct?
anonymous
  • anonymous
what did u do to find the widest point??
anonymous
  • anonymous
I'm not sure if it's right. But i think this is a question that's easier than you would think. You want to find the widest point, so all I did was add 7,375 and 4,425 and that gives you 11,800.
anonymous
  • anonymous
are you sure about his

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