If 4x-3y=12 represent line l and 12x+5y=0 represents line l'. find the equation of the locus of P under the following condition :
1) P is twice as far from l as from l'
2) is equidistant from l and l'

Question

If 4x-3y=12 represent line l and 12x+5y=0 represents line l'. find the equation of the locus of P under the following condition :
1) P is twice as far from l as from l'
2) is equidistant from l and l'

anonymous · Answer

@amistre64

amistre64 · Answer

what have you tried?

anonymous · Answer

P(x,y)

amistre64 · Answer

2) should just be an average of the slopes, anchored to the point they have in common 

1) is more interesting id say

amistre64 · Answer

do you know any formulas that helps us define a points distance from a line?

anonymous · Answer

would that be the perpendicular one?$$|\frac{ Ax+By+C }{ \pm \sqrt{A^2+B^2} }|$$

amistre64 · Answer

yes, as long as you are allowed to use it

anonymous · Answer

yea we shd be

amistre64 · Answer

then set one distance to twice the other ... and simplify

anonymous · Answer

do we equate them? which one shd be twice though?

amistre64 · Answer

l is 2 times longer than l'  ... as given in the information

amistre64 · Answer

l = 2l'

amistre64 · Answer

and i believe your formula is for a line of the form:

Ax + By + C = 0

anonymous · Answer

but... l is 2 times longer than l' ...i was thinking 2l=l'..lol

amistre64 · Answer

d1 = distance to l
d2 = distance to l'

 P is twice as far from l (d1) as from l' (d2)

d1 = d2 + d2

amistre64 · Answer

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