Thread: Equation of the graph

Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27.


anybody please

the distance from (0,3) to the vertical line x = 27 is 27 ... 1/3 of that distance is 9.

now, what do you call the set of all points that are a distance 9 from the point (0,3) , and further ... what is its equation?


also, contrary to what you may think, this is not advanced algebra ... in future, post a problem like this in the Precalculus forum.

Originally Posted by rcs

Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27.

My guess is that the word "graph" should be replaced by "locus." More importantly, the question seems to be about points whose distance from (0, 3) is 1/3 of their distance to x = 27, not 1/3 of the distance between (0, 3) and x = 27.

After writing the equation, this seems to be an ellipse according to the classification of conic sections.

Originally Posted by rcs

Find the equation of the graph of all points whose distances from ( 0, 3) are 1/3 of their distances from the line x = 27....

Hello, rcs!

Did you make a sketch?

Find the equation of the graph of all points whose distances from (0, 3) are 1/3 of their distances from the line x = 27.

Code:

      |
      |                       :
      |   (x,y)               :B
      |     o  *  *  *  *  *  o(27,y)
      |   * P                 :
     A| *                     :
 (0,3)o                       :
      |                       :
      |                       :
      |                       :
  - - + - - - - - - - - - - - + - -
      |                      27

We have point

Its distance from is: .

Its distance from the line is: .

We are told that is one-third of

So we have the equation: .

Now simplify the equation and identify the graph.

sir where did you get the 1/2 ? when the problem states for the 1/3 ?

Originally Posted by rcs

sir where did you get the 1/2 ? when the problem states for the 1/3 ?

1/2 in post #5 is a typo.

what do you mean typo? i dnt think there is 1/2 in there

Typo means he typed it incorrectly = typed it wrong = typed it by error = not typed correctly = big finger typed = .....

Thank you MaxJasper ... you are the best