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

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- Sep 9th 2012, 04:35 AMrcsEquation 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 - Sep 9th 2012, 04:45 AMskeeterRe: 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. - Sep 9th 2012, 10:53 AMemakarovRe: Equation of the graph
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. - Sep 9th 2012, 11:48 AMMaxJasperRe: Equation of the graph
$\displaystyle \pm \sqrt{x^2+(-3+y)^2}=-9+\frac{x}{3}$

http://mathhelpforum.com/attachment....1&d=1347220061 - Sep 9th 2012, 12:18 PMSorobanRe: Equation of the graph
Hello, rcs!

Did you make a sketch?

Quote:

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

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.

- Sep 10th 2012, 06:18 AMrcsRe: Equation of the graph
sir where did you get the 1/2 ? when the problem states for the 1/3 ?

- Sep 10th 2012, 06:57 AMemakarovRe: Equation of the graph
- Sep 10th 2012, 06:30 PMrcsRe: Equation of the graph
what do you mean typo? i dnt think there is 1/2 in there

- Sep 10th 2012, 08:02 PMMaxJasperRe: Equation of the graph
Typo means he typed it incorrectly = typed it wrong = typed it by error = not typed correctly = big finger typed = .....

- Sep 10th 2012, 11:02 PMrcsRe: Equation of the graph
Thank you MaxJasper ... you are the best