Conics question (1 Viewer)

[dawso]

swear the book is wrong, heres the question.... thanx guys

Find the locus of the point (x,Y) which moves so that its distance from (0,4) is two times its distance from y=1

 

[KFunk]

√( x² + (y - 4)²) = 2(y - 1)

x² + (y - 4)² = 4(y - 1)²

x² + y² - 8y +16 = 4y² - 8y +4

x² - 3y² +16 = 4

3y² - x² = 12

y²/4 - x²/12 = 1

 

[dawso]

fare enuf mr funk, btw, bring back ur old avatar, the dancing bear, that was gold!

next question, lol...

P lies on the hyperbola (x^2)/9 - (y^2)/72 = 1 with foci s and s'

if PS = 2 find PS'

 

[FinalFantasy]

fare enuf mr funk, btw, bring back ur old avatar, the dancing bear, that was gold!

next question, lol...

P lies on the hyperbola (x^2)/9 - (y^2)/72 = 1 with foci s and s'

if PS = 2 find PS'

x²\9-y²\72=1
72=9(e²-1)
72\9=e²-1
9=e²
.: e=3
let M be perpendicular foot of PM, M(a\e, y1)=(1, y1)
PS\PM=e
PS=ePM=3PM=2
.: PM=2\3
PM²=(x1-1)², PM=x1-1=2\3, .: x1=5\3
let M' be da foot at other directrix, i.e M'=(-1, y1)
PS'\PM'=3
PS'=3PM'
PM'²=(5\3+1)², PM'=8\3
PS'=3*8\3=8

 

[LaCe]

good stuff with the conics though.
with the line y=1 u expressed it as (y-1) when doing the locus bit... are u sure u r right? probably are eh?

 

[dawso]

ok, well i got that at 14 for when PS = 8, but i dont get how u can get 8, 14 or 2nas the book says...

 

[dawso]

ahh my bad, it will be 2 when the distance to the opposite focus is 8, tricky mr arnold...

 

[KFunk]

K Funk, ur avatar should be "you're retarded", im guessing ur not the best english student

Haha. Please tell me you didn't just walk into that trap...

EDIT: See website

http://www.bustedtees.com/product.php?name=yourretarded

 

[FinalFantasy]

ok, well i got that at 14 for when PS = 8, but i dont get how u can get 8, 14 or 2nas the book says...

huh? i am confuse now lol

 

[dawso]

lol, yeah i confused myself with what i said, ok, the question is from cambridge, it asks u to find PS' when a) PS = 2 and when b)PS = 8, as an answer it 2, 8, 14 for all of it...

the way this comes is because S isnt nececarily the closest focus, it can also be the far focus and hence PS' will be less than PS....

 

[dawso]

Haha. Please tell me you didn't just walk into that trap...

EDIT: See website

http://www.bustedtees.com/product.php?name=yourretarded

very nice.... i take back what i said, new avatar is better than last one

 

[FinalFantasy]

oh in cambridge, they put a ; to indicate that it's for another part.
e.g it probably said 8; 2,14 or something

 

[dawso]

oh in cambridge, they put a ; to indicate that it's for another part.
e.g it probably said 8; 2,14 or something

ah yes, on closer inspection, "8; 2 or 14"