anonymous
  • anonymous
Anyone good at parabolas? If so, Help please :) (a) Write down the equation of the chord of contact of the parabola x^2 = 4ay from the point P(x0, y0 ), then write it in gradient–intercept form y = mx + b. (b) Let this chord meet the axis of the parabola at T, and let the line through P parallel to the axis meet the parabola at N. Use part (a) to show that: (i) the points P and T are equidistant from the tangent at the origin, (ii) the chord is parallel to the tangent to the parabola at N.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I have done part (a) already
anonymous
  • anonymous
Just confirming, you need help with part b now?
anonymous
  • anonymous
yep

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anonymous
  • anonymous
Alright, give me a second to process what this is asking.
anonymous
  • anonymous
|dw:1377862033767:dw|
anonymous
  • anonymous
What did you get for part a? Can you put it on the board?
anonymous
  • anonymous
The problem says use the result from part a to solve the other parts of the problem
anonymous
  • anonymous
|dw:1377862234951:dw|
anonymous
  • anonymous
|dw:1377862308001:dw|
anonymous
  • anonymous
@hartnn @satellite73 help please :)
anonymous
  • anonymous
i am sure we can do this, i just have to figure out what is says i spent all this time doing a, but already did it
anonymous
  • anonymous
ok cool :)
anonymous
  • anonymous
ok i am a little slow today lets look at this line Let this chord meet the axis of the parabola at T since the parabola is \(4ay=x^2\) the axis of the parabola is the \(y\) axis if i am not mistaken that means that T is the \(y\) intercept right?
anonymous
  • anonymous
yea i agree
anonymous
  • anonymous
|dw:1377868921050:dw|
anonymous
  • anonymous
|dw:1377868964153:dw|
anonymous
  • anonymous
i am sorry i can't for the life of me figure out what this question is asking maybe for my feeble mind we could do an actual example with actual numbers then maybe if i can figure out what the question is, we can do it with variable
anonymous
  • anonymous
lol ok
anonymous
  • anonymous
ooh i think i see what it is saying!!
anonymous
  • anonymous
this line the points P and T are equidistant from the tangent at the origin, made no sense to me P is ON the tangent line, so its distance from the tangent line is zero!!
anonymous
  • anonymous
what i think it should say is that the point P and T are equidistant from the origin!!
anonymous
  • anonymous
hmm.. When it said it is equidistant from the tangent at the origin, I think it meant from the x axis
anonymous
  • anonymous
well i know that is what is says, but the first part asks you to find the equation of the line tangent to the parabola at the point P right?
anonymous
  • anonymous
|dw:1377869752569:dw|
anonymous
  • anonymous
i think that is what is asking you to show
anonymous
  • anonymous
hmm ok, ill try that
anonymous
  • anonymous
if it is true it should not be that hard, because since T is the y intercept, then the distance is just that number
anonymous
  • anonymous
wait, i think your diagram is incorrect because.. It says chord of contact
anonymous
  • anonymous
|dw:1377870448960:dw|
anonymous
  • anonymous
|dw:1377870483879:dw|
anonymous
  • anonymous
|dw:1377870621427:dw| This is P
anonymous
  • anonymous
ooh ok i see what you are saying
anonymous
  • anonymous
Those 2 lines up above were the tangents not the chord of contact.. Well thats what i think anyways
anonymous
  • anonymous
well this is certainly helpful http://www.youtube.com/watch?v=nMXyVD5b5rA
anonymous
  • anonymous
you are right
anonymous
  • anonymous
|dw:1377870998772:dw|
anonymous
  • anonymous
slowly i see it sorry i wasted your time above
anonymous
  • anonymous
|dw:1377871086721:dw| So... this diagram is correct right?
anonymous
  • anonymous
its ok @satellite73 :)
phi
  • phi
I think (b) means the vertical distance from T to the x-axis (tangent of the parabola) and the vertical distance from P to the x-axis P is at (x0,y0) and its distance is y0 T is at -y0 and its distance is also y0
phi
  • phi
I had to look up "chord of contact" http://www.askiitians.com/iit-jee-coordinate-geometry/tangent-to-a-parabola-page4.aspx
anonymous
  • anonymous
correct me if i am wrong T is where the line crosses the \(y\) axis, i.e. where \(y=0\) so the coordinates of T are \((\frac{2ay_0}{x_0},0)\)
phi
  • phi
for (c), point N has x-coordinate of x0 (same as P) the slope of the tangent at x0 is given by dy/dx = x0/2a which matches the slope of the "chord of contact"
phi
  • phi
the equation of the "chord of contact" is y = (x0/2a) x -y0 (assuming Teemo did that correctly) the y-intercept is -y0
anonymous
  • anonymous
yawn... Its midnight in Australia :( lol so tired....
anonymous
  • anonymous
@phi thanks i was totally stumped
anonymous
  • anonymous
i checked the back of my book and yes i got part(a) right.
phi
  • phi
|dw:1377871568884:dw|
anonymous
  • anonymous
so its the distance to the x-axis NOT the origin?
phi
  • phi
(b) is asking for the distance from a point to a line (the line y=0)
anonymous
  • anonymous
ahhh ok
phi
  • phi
The writing is a clear as mud, but (1) a tangent line is a line, so I assume that is what they mean. (2) both points P and T are a distance y0 from the tangent line, which sounds like what they are asking
anonymous
  • anonymous
ok :D thanks for you help!!

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