# Thread: Equation of the graph

1. ## 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.

2. ## Re: Equation of the graph

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.

3. ## Re: Equation of the graph

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.

4. ## Re: Equation of the graph

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....
$\displaystyle \pm \sqrt{x^2+(-3+y)^2}=-9+\frac{x}{3}$

5. ## Re: Equation of the graph

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 $\displaystyle P(x,y)$

Its distance from $\displaystyle A(0,3)$ is: .$\displaystyle PA \:=\:\sqrt{x^2 + (y-3)^2}$

Its distance from the line $\displaystyle x = 27$ is: .$\displaystyle PB \:=\:27-x$

We are told that $\displaystyle PA$ is one-third of $\displaystyle PB.$

So we have the equation: .$\displaystyle \sqrt{(x^2 + (y-3)^2} \:=\:\frac{1}{2}(27-x)$

Now simplify the equation and identify the graph.

6. ## Re: Equation of the graph

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

7. ## Re: Equation of the graph

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.

8. ## Re: Equation of the graph

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

9. ## Re: Equation of the graph

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

10. ## Re: Equation of the graph

Thank you MaxJasper ... you are the best