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.
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.
After writing the equation, this seems to be an ellipse according to the classification of conic sections.
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.We have pointCode:| | : | (x,y) :B | o * * * * * o(27,y) | * P : A| * : (0,3)o : | : | : | : - - + - - - - - - - - - - - + - - | 27
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.