let the dog's position be P(x,y)
Translate the English into math :
"..it is at all times twice as far from A as it is from B"
AP = 2BP
√[(x+2)^2 + (y-3)^2] = 2√[(x-4)^2 + y-6)^2]
square both sides, while expanding at the same time :
x^2 + 4x + 4 + y^2 - 6y + 9 = 4(x^2 - 8x + 16 + y^2 - 12y + 36)
reduces to x^2 - 12x + y^2 - 14y = 65
Do you recognize this to be the equation of a circle?
Can you find the centre and the radius anf draw the sketch or graph from there?
in the backyard there are two trees located at grid points A(-2,3) and B(4,-6)
a) The family dog is walking through the backyard so that it is at all times twice as far from A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog and the relationship defining the locus. Then write a geometric description of the path od the dog relative to the two trees.
b) The family cat is also walking in the backyard. The line segment between the cat and the two trees are always perpendicular. Find the equation of the locus od the cat. Draw a graph that shows the path of the cat. Then write a geometric description of the path of the cat relative to the two trees.
Hey guys, i was wondering if anyone can help me get started with these two questions. Usually, i i don't have that much problems with this chapter, but when dealing with word questions, i get lost. Thanks for your help. Alley
4 answers
For the second question, if we again let P(x,y) be any position of the cat
isn't the slope of AP always the negative reciprocal of the slope of BP?
Let me know what you got as an equation.
isn't the slope of AP always the negative reciprocal of the slope of BP?
Let me know what you got as an equation.
AP = 2BP
�ã[(x+2)^2 + (y-3)^2] = 2�ã[(x-4)^2 + y-6)^2]
maybe it's just me, but shouldn't be
�ã[(x-2)^2 + (y+3)^2] = 2�ã[(x+4)^2 + y-6)^2]
�ã[(x+2)^2 + (y-3)^2] = 2�ã[(x-4)^2 + y-6)^2]
maybe it's just me, but shouldn't be
�ã[(x-2)^2 + (y+3)^2] = 2�ã[(x+4)^2 + y-6)^2]
Just saw your reply now.
I did the question on a piece of paper before typing in the solution and
inadvertently wrote down the point B(4,-6) as (4,6)
so the equation I had written as
√[(x+2)^2 + (y-3)^2] = 2√[(x-4)^2 + y-6)^2]
should have been
√[(x+2)^2 + (y-3)^2] = 2√[(x-4)^2 + y+6)^2]
make the necessary changes in my solution, the only change would be in the y term.
I did the question on a piece of paper before typing in the solution and
inadvertently wrote down the point B(4,-6) as (4,6)
so the equation I had written as
√[(x+2)^2 + (y-3)^2] = 2√[(x-4)^2 + y-6)^2]
should have been
√[(x+2)^2 + (y-3)^2] = 2√[(x-4)^2 + y+6)^2]
make the necessary changes in my solution, the only change would be in the y term.
1 answer