DAT Bootcamp giving incorrect answer to their own problem?

[basserpa]

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So I purchased DAT Bootcamp yesterday, got through a couple exams but then on my second QR exam, this came up:
38. In the figure below, an elliptical mirror has foci A and B with respective coordinates (-4,0) and (4,0). The minor axis of the ellipse is 6 units long. A ray of light travels 7 units as it passes from focus A to point Q on the mirror’s surface. The light ray then reflects off point Q and travels to focus B. What is the distance from point Q to focus B?

• A. 7
• B. 5
• C. 3√2
• D. 3
• E. 2

DAT Bootcamp's Explanation: Do not trust the pictures to be scaled correctly. Triangle AQB is not a right triangle. The origin, focus A, and the top endpoint of the minor axis define a 3-4-5 right triangle. The same is true for the origin, focus B, and the top endpoint of the minor axis. If point Q were located at the top endpoint of the minor axis and reflected a ray of light from focus A to focus B, the light would travel along the hypotenuses of both 3-4-5 triangles, a total distance of 10. No matter where point Q is actually placed on the ellipse, the reflected path from A to Q to B will always be 10. This is one definition of an ellipse. If the distance from A to Q is 7, the distance from Q to B must be 3.

My spiel: Bootcamp's answer would be right if we had a minor axis of 5, but it's 6. You'de get 2sqrt(52) as a total distance from the two foci, not 10, and there's no 3-4-5 triangle being made, especially because theres a minor axis of 6.

How I solve: So if we consider points Origin, Foci, and Minor axis endpoint, we would have a right triangle that has dimensions of 4, 6, and a hypotenuse, which we can solve for by using pythagorean and get sqrt(52). Thus the distance from one foci to the top endpoint is sqrt(52) and we got two foci, so make it 2sqrt(52), not 10. If the distance A to Q was 7, then the length from Q to B = 2sqrt(52)-7.

At least they correctly got the part where you assume that light reflects in that fashion, incident upon that surface at some angle (not that we need the physics here). How we feeling?

 

[ywcywc]

I think you confuse the minor axis to semi minor axis. 6 is minor axis, semi minor axis is 6/2=3.

 

[basserpa]

I think you confuse the minor axis to semi minor axis. 6 is minor axis, semi minor axis is 6/2=3.

I appreciate the clarification, thank you for making that very clear.

 

[PocketRocket]

Lol I made the same mistake you did and for like a minute was mad at bootcamp for making a mistake that big. But then I realized it's the Minor not semi-minor.. I catch myself doing the same thing with destroyer problems but I've learned that these products are pretty much error free.