lilsis76
  • lilsis76
11.2 the Parabola. Its says Conic sections: suppose PQ is a focal chord of the parabola y=x^2 and that the coordinates of P are (2,4) a)find coordinate of Q b)find coordinates of M, the midpoint of PQ. c) A perpendicular is drawn from M to the y axis, meeting the y axis at S. Also, a line perpendicular to the focal chord is drawn through M, meeting the yaxis and T. Find ST, and verify its equal to one-half the focal width of the parabola.
Mathematics
schrodinger
  • schrodinger
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lilsis76
  • lilsis76
|dw:1352584620353:dw|
lilsis76
  • lilsis76
|dw:1352584696851:dw|
lilsis76
  • lilsis76
whats a focal chord? I was givin this homework problem and instructor confused me on all the different positions

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anonymous
  • anonymous
Any chord to y2 = 4ax which passes through the focus is called a focal chord of the parabola y2 = 4ax.
anonymous
  • anonymous
@lilsis76 tell me the focus of ur parabola?????:)
lilsis76
  • lilsis76
well, it didnt give me a focus it just gave me the P at (2,4)
lilsis76
  • lilsis76
it also says the parabola is y=x^2 so...um the p, 1/4
anonymous
  • anonymous
@lilsis76 focus of x2 = 4ay is(0,a) so compare it with x^2=y this implies 4a=1 or a=1/4 so it is(0,1/4).k
lilsis76
  • lilsis76
okay im back!
anonymous
  • anonymous
now you have 2 points p(2,4) and focus f(0,1/4) so can u draw a line???????????
lilsis76
  • lilsis76
yes i can
lilsis76
  • lilsis76
|dw:1352585497197:dw|
anonymous
  • anonymous
so thats ur focal chord any chord passing through focus is called focal chord:)
lilsis76
  • lilsis76
let me write that down
lilsis76
  • lilsis76
did i make the line right?
anonymous
  • anonymous
ya you make it right:) sry i didn't noticed ur reply:( @lilsis76
lilsis76
  • lilsis76
haha its okay. but thank u for letting me know. Okay whats next what do i have to do?
anonymous
  • anonymous
|dw:1352586259141:dw| now what is the coordinate of any point on parabola?????
lilsis76
  • lilsis76
wait, its a normal looking parabola with the point (0,0) right? thats how you got that parabolas shape?
lilsis76
  • lilsis76
im sorry im kinda new to this lol
lilsis76
  • lilsis76
since you said any point. ill go to the left. the Q would be P's opposite and be .. -2,4? right?
anonymous
  • anonymous
well it is not what i asked i asked general form it is(x,x^2) :) as PFQ is a straight line so slope of PF=FQ now find their slopes...........when u solve this completely i will tell you a short method:)
anonymous
  • anonymous
@lilsis76
lilsis76
  • lilsis76
okay. im trying to do PF, is that ...getting the 2*1/4?
anonymous
  • anonymous
PF??????????
lilsis76
  • lilsis76
hmm... let me try again
lilsis76
  • lilsis76
1/4th?
lilsis76
  • lilsis76
WAIT let me try again
lilsis76
  • lilsis76
i got..... 4 - 1/4 / 2-0
lilsis76
  • lilsis76
|dw:1352587321957:dw| i dont know how to work out the fraction and whole number
anonymous
  • anonymous
slope m=|dw:1352587256238:dw| solve for x i just compare the two slopes:)
lilsis76
  • lilsis76
15/4/2--> 15/8
lilsis76
  • lilsis76
@Aperogalics
anonymous
  • anonymous
@lilsis76 is it value of x?????????
lilsis76
  • lilsis76
yes? how do i know?
anonymous
  • anonymous
i have to solve:(
lilsis76
  • lilsis76
oh. well then imma say yes it is then
anonymous
  • anonymous
|dw:1352587871193:dw|
lilsis76
  • lilsis76
how did you get the 13/8?
anonymous
  • anonymous
|dw:1352588075547:dw| so x=-1/8 or 2
lilsis76
  • lilsis76
haha okay. thanks
lilsis76
  • lilsis76
ugh factoring
anonymous
  • anonymous
coordinates are (x,x^2) from fig x<0 x cannot be =2 Q=(-1/8,1/16)
lilsis76
  • lilsis76
okay i got the -1/8
lilsis76
  • lilsis76
and the 2, did you just add the 1/8 th twice to get 1/16?
anonymous
  • anonymous
now shortcut method:) Let y2 = 4ax be the equation of a parabola and (at^2, 2at) a point P on it. Suppose the coordinates of the other extremity Q of the focal chord through P are (at1^2, 2at1). then t1=-1/t:) so |dw:1352588333605:dw|
anonymous
  • anonymous
no @lilsis76 as the coordinates are(x,x^2)
anonymous
  • anonymous
@lilsis76 did u got it?????????
lilsis76
  • lilsis76
kinda, not really. okay well i ended up getting the - 1/8 for x, i plug it in right?
anonymous
  • anonymous
yup:)
lilsis76
  • lilsis76
ok i got 8x+1 an x-2, x= -1/8, x=2
anonymous
  • anonymous
now go ahead for shortcut:)
lilsis76
  • lilsis76
the shortcut u gave me?
anonymous
  • anonymous
yup:)
lilsis76
  • lilsis76
i got -1/8
lilsis76
  • lilsis76
@Aperogalics
lilsis76
  • lilsis76
anywho, i did the math cuz shortcut got me lost. i have x = -1/8 and x=2

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