QR ADA 2009 question

[299678]

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? (no picture was given)

---

Members don't see this ad.

 

[hausee]

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? (no picture was given)

2*sqrt(20)

actually light start from one focus reflected to another focus will have travel distance of 2*sqrt(20), no matter what route it takes.

 

[hausee]

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? (no picture was given)

by the way, Kpark, next time you should list choices.

 

[299678]

a) square root 3
b) ssquare root 5
c) square root 10
d) square root 12
e) square root 20

This was the reason why I posted this problem.

 

[299678]

Determine the sets of points whose distance from (-2,2) and (3,-3) are in the ratio of 2:3

answer is
b) circle with center (-6,6) with radius 6*square root 2

I need a reasoning for the question.

 

[hausee]

a) square root 3
b) ssquare root 5
c) square root 10
d) square root 12
e) square root 20

This was the reason why I posted this problem.

Hahaha, I too have ADA 2009 sample test. It has a lot of errors. I heard some SDNers joking that ADA want you to work harder to find out their errors...😀

 

[299678]

hahahah 🙂 thanks

 

[hausee]

Determine the sets of points whose distance from (-2,2) and (3,-3) are in the ratio of 2:3

answer is
b) circle with center (-6,6) with radius 6*square root 2

I need a reasoning for the question.

Man, this gonna take at least 3 mins if you follow my method. Anyway, you asked for it...

suppose (x,y) satisfy the requirement.

distant from (x,y) to (-2,2): sqrt[(x+2)^2+(y-2)^2]=a
distant from (x,y) to (3,-3): sqrt{(x-3^2+(y+3)^2]=b

a/b=2/3

(a/b)^2=(2/3)^2=4/9

substitute a and b then cancel out extra you will get :

x^2+12x+y^2-12y=0

look closely, you will find x^2+12x=(x+6)^2-36
same, y^2-12y=(y-6)^2-36

so x^2+12x+y^2-12y=(x+6)^2+(y-6)^2-36-36=0

move two 36 to the right, you get

(x+6)^2+(y-6)^2=2*36

now it look familiar? it represent a circle with center (-6,6), and radius with sqrt(2*36)=6*sqrt(2)



hewwww.....🙂

 

[skype]

This is not the type of questions on the test is it?????

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? (no picture was given)

 

[hausee]

This is not the type of questions on the test is it?????

I got a ellispe Q

 

[dreamerndoer]

#4 on 2009
In the figure, the horizontal incident ray 1 strikes the circular mirror, x^2 + y^2 = 25, resulting in the reflected ray R. What is the y coordinate of the intersection point of the ray R and the line x = 12 ?? You may need to use the identity tan2(theta) = 2tan(theta)/1(1-tan^2(theta))

Also, #6

 

[Gomsemari]

2*sqrt(20)

actually light start from one focus reflected to another focus will have travel distance of 2*sqrt(20), no matter what route it takes.

can someone explain why it's 2*sqrt(20) ???
i have no clue how to solve this problem... please help

 

[Gomsemari]

ahh ok i was searching google, and on the wiki, it says " The foci of the ellipse are two special points F1 and F2 on the ellipse's major axis and are equidistant from the center point. The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major diameter ( PF1 + PF2 = 2a ). Each of these two points is called a focus of the ellipse." with a picture/graph. the website is : http://en.wikipedia.org/wiki/Ellipse or u can just type ellipse on google.

so the answer to this question is square root of 20 no matter what route it takes.
hmm i didnt know we had to know this for dat... o wells. at least i figured it out.
hmm i posted a question, and answered it myself, cool

 

[Gomsemari]

#4 on 2009
In the figure, the horizontal incident ray 1 strikes the circular mirror, x^2 + y^2 = 25, resulting in the reflected ray R. What is the y coordinate of the intersection point of the ray R and the line x = 12 ?? You may need to use the identity tan2(theta) = 2tan(theta)/1(1-tan^2(theta))

Also, #6

another question !
for number 4, i tried, but cant figure it out.
can someone please explainnnnn??

 

[letsgetit2124]

The answer is actually sqrt20

The distance from "foci-1" to a point on the ellipse and back to "foci-2" is always equal to "2a" where "a" is equal to HALF the major axis length.

In this case, the major axis length (2a) is equal to sqrt20 as given in the problem. So "a = sqrt20/2" or in other words, "2a/2", or in other words, "half of 2a", or in other words, simply "a". So if the distance from "foci-1" to a point and back to "foci-2" is twice that, or "2a", then the distance is (sqrt20 / 2) x 2. Conveniently, the answer is sqrt20.

Shortcut, if you really understand how an ellipse works, you realize that the distance from a foci to ANY point and back to the other foci is ALWAYS ALWAYS ALWAYS equal to 2a and 2a is equal to the MAJOR axis length. **Note: 2a is always the length of the LONGEST axis, hence the name MAJOR. so if the ellipse is short and fat, the long axis is in the x direction. If the ellipse is tall and skinny, the long axis is in the y direction. This did not come into play in our question b/c they directly stated "major axis length" instead of "a" or "b." If you are curious why it is ALWAYS the length of the major axis, its b/c the foci are always placed on the longest axis (major axis) so thats why the concept revolves around what "a" is and not so much what "b" is.

Hope that helps