Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
vf321
Group Title
Define the region \(\Sigma\subset\mathbb{R^2}\) as a system of inequalities for \((x, y)\). \(\Sigma\) is the intersection between the two regions defined by the ellipses (1) and (2)  see below for equations. Assume that the ellipses intersect.
 2 years ago
 2 years ago
vf321 Group Title
Define the region \(\Sigma\subset\mathbb{R^2}\) as a system of inequalities for \((x, y)\). \(\Sigma\) is the intersection between the two regions defined by the ellipses (1) and (2)  see below for equations. Assume that the ellipses intersect.
 2 years ago
 2 years ago

This Question is Closed

vf321 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{y^2}{y_1^2}+\frac{x^2}{x_1^2}=1\]\[\frac{y^2}{y_2^2}+\frac{(xx_0)^2}{x_2^2}=1\]As stated in assumptions, \(x_0>x_1x_2\), and the resulting inequalities may be expressed in terms of all subscripted constants.
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
It's also okay to express the inequalities for x in terms of y, seeing as this is a type II region.
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
@lgbasallote @Hero @jim_thompson5910 @dumbcow Anybody mind helping please? No one's answered for 2 hours.
 2 years ago

panlac01 Group TitleBest ResponseYou've already chosen the best response.0
@hero is here to save the day
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
x_0 is a point, x_1  x_2 is a distance
 2 years ago

panlac01 Group TitleBest ResponseYou've already chosen the best response.0
@Geometry_Hater
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
@experimentX x_0, x_1, x_2, y_1, y_2 are all scalars
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
okay, I guess I'm going to Math.SE again!
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
i would take each ellipse equation and solve for "y^2" then set them equal in order to get it in terms of x rearrange terms and finally solve for x_0 ...it gets messy with so many constants then substitute that expression into inequality .... x_0 > x_1 x_2 then rearrange terms again to solve for "x" using quadratic formula
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
Yes that would get us the two points of intersection, I agree. I can do that. But that still doesn't define the area.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
what do you mean? you have to find the area of the region
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
i thought you had to define the region with inequalities... a<x<b and c<y<d is that right
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
Yes. But say I have to elipses: dw:1346028226442:dw I admit that we can find a, b, and c. But how does that help us find the region in the middle?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
why not use piece wise functions ??
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
dw:1346028684685:dw the region in middle is defined as e < x < f b < y < c
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
That's a rectangle
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
hmm...looks like i am no help :
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
It's okay. As soon as I put the question up on Math.SE I'll put up a link here if you are interested.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
oh i have been approaching it wrong if you define each ellipse as function of y....f(y) and g(y) then using your picturedw:1346029715377:dw f(y) < x< g(y) c < y < b
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
I already thought about it that way. Unfortunately, it wouldn't work: dw:1346029850266:dw Unless you want to break that up into a type II region and two type Is, that's not gonna help
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
My suggestion would be to try polar although that has not given me any success so far.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
we can assume the region is symmetric about xaxis correct ?
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
We know for a fact even
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
hmm ok im done :) last thought then is you have to break it up into different cases of possible regions
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
yes thats what I said you could do. But we'll see what SE says. I'll post the link soon.
 2 years ago

panlac01 Group TitleBest ResponseYou've already chosen the best response.0
good job @dumbcow
 2 years ago

panlac01 Group TitleBest ResponseYou've already chosen the best response.0
you sir, are the best
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
http://math.stackexchange.com/questions/187316/howcanidefinetheareabetweentwoellipses
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.