Question

a double ordinate parabola (y^2)=2ax is of length 4a.... prove that the lines joining the vertex to its ends are at right angles

Answer 1

i dont understand the term length is 4a in this questio n..please explain me and also answer

Answer 2

what is your understanding of a double ordinate?

Answer 3

could you give me an example of where that is on a parabola?

Answer 4

a double ordinate is a line segment parallel to the latus rectum.

Answer 5

i don't know these terms lol

Answer 6

i mean i know what a line segment and parallel means

Answer 7

aa ok....but what is that 4a ?

Answer 8

yeah what are these terms? o.O google google.

Answer 9

lol joe

Answer 10

also in this question y^2=2ax... General equation is y^2=4ax.. So the coordinates of focus will change and will not be a,0

Answer 11

a/2,0 is the focus of the parabola
..

Answer 12

so u can consider the end points of the double ordinate to be At^2,2At.. Where t is the parameter and A=a/2 the abcissca of the focus

Answer 13

then u can take 4At=4a that is the length of the double ordinate.. solve it to get t

Answer 14

then use pythagoras to prove its a right angled triangle at origin using distance formula to find the length

Answer 15

hope you can do it from here.. :)

Answer 16

does anyone know where i can find a visual explanation of the double ordinate?
i tried to google but failed

Answer 17

me too, these seem to be really old terms >.<

Answer 18

oh.. wait i will try to create a visual representation..

Answer 19

:)

Answer 20

http://ginryuukurochan.wordpress.com/2007/09/26/parabola/ in the pic of parabola DD' is the latus rectum n a line segment parallel to it is a double ordinate

Answer 21

i drew a picture of what i think is going on lol <.<
and i used vectors and a dot product to show the two segments are perpendicular. One sec while i scan~

Answer 22

If theres something wrong or if the picture is totally off let me know. As far as i could tell, the double ordinate is just a segment from the parabola to the axis of symmetry that is perpendicular to the axis.

Answer 23

gotta love that misspelling of perpendicular in the drawing <.< im slightly intoxicated, its not my fault >.>

Answer 24

lol
you guys are so cool
i guess we can call these geometry terms
thanks for giving me a clearer understanding of them both of you

Answer 25

latus rectum, sounds gross >.>

Answer 26

i know
i thought he was kidding on the name earlier

Answer 27

ya a good one joe...

Answer 28

sry if i sound immature >.< im normally more intelligent sounding! i promise!

Answer 29

lol

Answer 30

sure you are

Answer 31

But was that picture correctly drawn? thats what im worrying about.

Answer 32

i am! i think >.>

Answer 33

i think it looks good but i dont know what im talking about

Answer 34

thats enough for me lol, its good!

Answer 35

i think its right...

Answer 36

where is the rectum of the parabola? lol

Answer 37

how come u guys dunno latus rectum??/ its official term.. which grades are u in?

Answer 38

@Akshay Thank you :)
@myininaya lol

Answer 39

i have a masters in math lol

Answer 40

Im a lowly undergraduate.

Answer 41

never heard of that term or the double ordinate or the ordinate

Answer 42

Me either, well, the last time ive officially played with parabolas is high school...in 01' 02'

Answer 43

i guess depending on which school you go to
you learn different things(i mean math is a huge subject its not like we can cover all of it)

Answer 44

oh... so i am privileged to help you guys..I jus did my 12th grade.:)

Answer 45

wow
what country?

Answer 46

we are from usa
we dont know crap

Answer 47

lol

Answer 48

im trying to make up for that! i read lol

Answer 49

i am from india.. moving to canada now... for engineering...

Answer 50

i wish we learned more advanced things in high school
i only got to alittle bit of algebra in high school never heard of a proof until college

Answer 51

my high school sucked

Answer 52

Mine too.

Answer 53

They just taught up to past standardized tests. Nothing more.

Answer 54

us* <.<

Answer 55

all we did in my ap english class was crossword puzzles

Answer 56

SATs?

Answer 57

nope. They didnt even teach us at that level. Some states in the US have standardized testing. Its unique for each state. But the level of it is really really really really low.

Answer 58

hehe.. u guys to have a sort of hatred towards ur high schools...

Answer 59

Its because they cheated us!

Answer 60

yes us
we could have been like you and knew what a freaking latus rectum was but no
i barely knew what a quadratic equation was

Answer 61

i know what it is now lol i'm talking about when i got done with high school

Answer 62

I wish there had been a class on proofs. Just the basic ones. Like "prove square root of 2 is irrational", or "Give a proof of why you cant divide by 0", or "Prove that there is no such number that is both even or odd".
I hate my school! argargarg.

Answer 63

but now ur a undergraduate no/?? From where? which field?

Answer 64

i was so envious of the chinese math grads
they knew so much more than us americans
and they caught on quicker than us
its like they already knew the stuff and it was elementary to them

Answer 65

i believe even we Indians are also very fast thanks to concepts of vedic maths if you know?

Answer 66

i just googled it lol, interesting o.O

Answer 67

i think there was one or two indian math grads
they were smarter than us as well
everyone is
:(

Answer 68

joe you should run for president and change our education system ok?

Answer 69

hehe.....

Answer 70

i think i can do that without running for president lol >.<

Answer 71

call yourself joemath
i think it is catchy and everyone will be like omg joemath is smart because he has math in his name

Answer 72

er...attempt to, thats what i meant.

Answer 73

hahaha

Answer 74

people on the streets will vote for you because they know they cant add 2 to 3
and they know you will be able to do 2+3

Answer 75

hehe... U guys seem to b quite determined to change the system... hope to see reforms in d cumin years.. :)

Answer 76

Where were you guys a few days ago >.> there were some people ganging up on me about the answer to a question. It was, "How many solutions are there to the equation:
\[\sqrt{x} = -4\]"

Answer 77

lol i dont know if it is possible to change the system

Answer 78

0 solutions

Answer 79

0 real solutions..

Answer 80

yes 0 real solutions

Answer 81

right!! they were telling me x = 16 was a solution, and I tried my hardest to convince them, but they were acting like i was some crazy guy trying to spread lies and misinformation >.>

Answer 82

hehe.. missed the fun!!

Answer 83

lol poor joe all by himself

Answer 84

they must be taking it as root of 16 is +-4.. right?

Answer 85

did you show them the curve y=sqrt{x} and the line y=-4 have no intersection?

Answer 86

it was frustrating <.< i gave so many good reasons why there were no real solutions <.< I talked about when you square equations you create extraneous solutions. I talked about the graph of f(x) = sqrt(x) and g(x) = -4 not intersecting.
@Akshay yeah, thats probably what they were thinking.

Answer 87

ya xactly thats what i was gonna say

Answer 88

LOL yeah myininaya great minds think alike :P

Answer 89

so that didn't convinced them
how interesting

Answer 90

hehe.. i thot d same like you guys!

Answer 91

what happened finally?

Answer 92

The person that created the question ended up deleting it lol >.< i think he was trying to get help with another question, but there were probably 12-15 people in his old thread arguing about that problem haha.

Answer 93

ya how do we integrate root of sinx?

Answer 94

i asked it some1 gave me an elliptical answer... isn't there a normal method?

Answer 95

u'r a genius :D

Answer 96

not every integral has a "nice", "normal" answer. It might be something like that.

Answer 97

http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html look at this.. I tried but couldnt understand most of it :(