Area of Ellipse

[RSD2014]

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How do we find a to find Area of Ellipse?



Ok, I Figured out how to solve it. The 2 points at the base of the Triangle are 2 foci.
According to the ellipse concepts, the sum of the distance from point b to each foci is equal to 2a.

Summarized: hypotenuse + hypotenuse = 2a
According to pythagorean, the hypotenuse will equal to 5
thus, 5 + 5 = 2a. a = 5.

Area of triangle = 1/2(4)(3) = 6
Area of the 2 Triangle = 12

Area of ellipse = pi(a)(b) = pi(5)(3) = 15pi

Area of Ellipse - Area of triangle = 15pi - 12

 

[gigawatt]

You won't need to know this, so don't worry about it.

Just for kicks...you would need to be told that those are the foci (which means that the diagram is horribly drawn). The value of a would be 5.

 

[kevinrho]

wait... so gigawatt you are saying we won't need to know about ellipse on the DAT? and i don't freakin understand anything on the image you posted... =/

 

[casper22]

Gigawatt.. great job explaining...only to those who understand it and I for sure am not one of them...

however instead of going through so much confusing explaination...

to find a why no use the information provided in the original diagram and then just calculate the largest side of a 30-60-90 triangle. That is 'a'.

 

[RSD2014]

Gigawatt.. great job explaining...only to those who understand it and I for sure am not one of them...

however instead of going through so much confusing explaination...

to find a why no use the information provided in the original diagram and then just calculate the largest side of a 30-60-90 triangle. That is 'a'.

Do you mean the hypotenuse of the triangle being a = 5? Shouldn't a be something like a = x+4? But the hypotenuse is ray AB, it is not a. Perhaps the diagram is not well drawn in the problem. I have never encountered this problem of all the math classes I have taken. Which is weird.

 

[hoylematt]

You know the Area of the Triangle: (1/2)(8)(3) = 12

A = major axis = ?
B = minor axis = 3
C = distance from origin to one Foci = 4

ABC are related by: A^2 = B^2 + C^2
Therefore: A = SquareRoot (9+16)
Therefore: A = 5

Area of an elipse = Pi(B)(A)
Area of this elipse = 15Pi

Therefore the Area of the elipse - the area of the triangle = 15pi - 12

Im actually kinda stoked i remembered that without looking at the math destroyer!

You won't need to know this, so don't worry about it.

I would have to disagree with this statement i specifically remember a tricky ellipse problem similar to this one on my first DAT and I was like WTF!

 

[Bio Dental Mom]

I got the same answer as the holymatt. I figured it out last night, but for some reason the forum was down yesterday?? I would add one more thing that the distance from the origin to one of the foci (in the picture depicted as "4") is your "c." So that's how it fits into the equation:

c^2= a^2 - b^2

I hope this helps, and yes, they had a couple of these throughout the math destroyer, so I would know this.

 

[gigawatt]

It looks like I spoke too soon. I'm surprised that people have seen this come up on the DAT based on how simple the QR questions I've seen have been, but then again asking for the area of an ellipse isn't too far beyond asking for the area of a circle. Sorry for the bad advice, and thanks to Bio Mom and hoylematt for setting it straight. 👍 🙂

 

[newmexomfs]

go to www.khanacademy.com and choose the ellipse video buddy! and u will be fine.

 

[Streetwolf]

you would need to be told that those are the foci

Yes!!!!

The problem never says these points are the foci. You can't assume they are! There isn't enough info to solve the problem as far as I can see. If someone sees something I missed please post it.

 

[gigawatt]

Yes!!!!

The problem never says these points are the foci. You can't assume they are! There isn't enough info to solve the problem as far as I can see. If someone sees something I missed please post it.

There isn't as far as I can see, either. If those aren't the foci, then it is just some random triangle that happens to have the same height...you don't have anything to on after that.

The diagram is horribly drawn (that's not what a 3x8 triangle would look like) and the English in the question is poor, not to mention the ???? overuse. I don't know where this problem came from, but it seems like a bad source.

 

[ZFT]

You won't need to know this, so don't worry about it.

Just for kicks...you would need to be told that those are the foci (which means that the diagram is horribly drawn). The value of a would be 5.

this is a nice graphical way to remember ...at least until after the DAT..... this interesting ellipse property.

for the original problem let point P = b then apply the 2a formula.

the general conclusion is that any triangle inscribed this way will have the two sides add up to the major diameter.