# Equation of the graph

• Sep 9th 2012, 04:35 AM
rcs
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.

• Sep 9th 2012, 04:45 AM
skeeter
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.
• Sep 9th 2012, 10:53 AM
emakarov
Re: Equation of the graph
Quote:

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.
• Sep 9th 2012, 11:48 AM
MaxJasper
Re: Equation of the graph
Quote:

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....

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

http://mathhelpforum.com/attachment....1&d=1347220061
• Sep 9th 2012, 12:18 PM
Soroban
Re: 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
We have point $P(x,y)$

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

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

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

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

Now simplify the equation and identify the graph.

• Sep 10th 2012, 06:18 AM
rcs
Re: 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 AM
emakarov
Re: Equation of the graph
Quote:

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.
• Sep 10th 2012, 06:30 PM
rcs
Re: Equation of the graph
what do you mean typo? i dnt think there is 1/2 in there
• Sep 10th 2012, 08:02 PM
MaxJasper
Re: 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 PM
rcs
Re: Equation of the graph
Thank you MaxJasper ... you are the best