Success One's solution incorrect? (1 Viewer)

[Saintly Devil]

For the 1984 Mathematics HSC Question 9) b)

"The point P(x,y) is equidistant from the lines y=3 3x+4y-18=0, and lies in the shaded region of the diagram.

Find the equation of the locus of P"

The anwer given by the Success One book's is y = -x/3 + 11/3. I got the answer y = -3x/8 + 30/8. Is the answer given by success one incorrect? because I graphed both equations and my answer was actually equidistant from the two lines given - not success one's.

Can someone clarify this?

 

[Viper]

I got the same answer as you...

But im not the greatest locus mathematitian going around...

Cheers

 

[Abide]

can either of you please post what you do to get the answer?
cos i really have nfi
lol

 

[LadyMoon]

You mean 1994? I remembered cause i did this paper a few days ago.

Apply the perpendicular distance formula, and the distance formula.
if X lies on y=3, then the coordinates of X(x,3)
therefore the distance from X to P is 3-y.

and the distance from P to the line 3x + 4y - 18=0 is equal to (3x + 4y -18)/5

equate the two:
5(3-y)=3x +4y -18

therefore y=-x/3 + 11/3
and x>2 (to satisfy the shaded region)

I got the same answer as the Book I use.
And i did graph it and according to WinPlot its looks correct, i tried your soultion also, you solution is not equidistant.

Furthermore how did you get that solution?

 

[Saintly Devil]

Yes, sorry, i meant 1994.

Hmm. yes, after once more considering, I think the solution given by Success One may be correct.

I did it by assuming that the locus would be a line with a gradient half that of 3x + 4y -18=0.

So I used the equation

3x + 4y -18 +k(y-3)=0
3x + y(4+k) -18 - 3k = 0

therefore the gradient of the line would be -3/(4+k)
As I assumed the gradient would be half of 3x + 4y -18=0 , I got

(-3/4 )2 = -3/(4+k)
k=4

sub into original equation

3x + 4y -18+ 4(y-3) = 0
y = -3x/8 + 30/8

But I can see this is wrong, because it assumes equidistant in terms of the y co-ordinates, not the actual perpendicular distance.
Thanks.

 

[LadyMoon]

No problem! Goodluck on Monday!