ADA 2009 Math #5

[monsieurwise]

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Hi everyone!
Sorry for this stupid question, but somehow I just can't figure out what does the question mean.

An elliptical mirror has foci at (+1,0), a major axis length of square root of 20, and a minor axis of length 4 units. A beam of light originating from the focus at (-1,0) is reflected of the elliptical mirror once before arriving at the other focus. What is the total length of the path followed by the beam of light?

a) sqrt(3)
b) sqrt(5)
c) sqrt(10)
d) sqrt (12)
e) sqrt (20)

I have no idea where to start because I can't even draw it out. Am I missing something super basic here? I got the foci-center distance to be 2 because c^2 = a^2 - b^2, but then why is there a "foci," then a "focus"?

Thanks so much everyone!!

 

[fifaplayer]

Not completely sure about this, but I think there is a relationship between the distance of the two foci in an ellipse and the value of the major axis. The distance between the two foci to any point of the ellipse is actually the major axis. Take a string which is loosely tied to both foci and, with a finger or a pencil, drag a segment of that string to any outer point of the ellipse (making sure the string is at full stretch)- the length of the string at any point will be the same and will be the length of the major axis. So i think the answer is E (sqrt 20).
Had a similar question in the Achiever a while ago. Obv got that wrong.. looked it up and tried the string thing (actually called the string and pin method).. never realized- pretty cool

 

[monsieurwise]

Ah I see it now =). Oh, but isn't the "major axis" is "a"? So then, shouldn't the answer be distance travelled = 2a = 2sqrt(20)?
Thanks!

 

[Illfavor]

"is reflected of the elliptical mirror"...? Is this a math term I'm unfamiliar with? Or a typo?