DLS
  • DLS
If P(-3,2) is one end of the focal chord PQ of the parabola y^2+ 4x + 4y =0, then the slope of the normal at Q is: (A) -1/2. (B) 2. (C) 1/2. (D) -2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
shubhamsrg
  • shubhamsrg
Whats your progress ?
DLS
  • DLS
\[\LARGE (y+2)^{2}=4(1-x) \] so vertex=(1,-2)
DLS
  • DLS
|dw:1359794353016:dw|

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More answers

DLS
  • DLS
this diagram is not possible :/ acc to what im thinking..
DLS
  • DLS
how can focus be (1,0)
DLS
  • DLS
\[\LARGE 2y \frac{dy}{dx}+4+4\frac{dy}{dx}=0\] i do everything i know :P because i dont know exactly what to do :o
DLS
  • DLS
\[\LARGE \frac{dy}{dx}=\frac{-4}{2y+4}\]
DLS
  • DLS
that is for tangent..
DLS
  • DLS
for normal it will be .. \[\LARGE \frac{2y+4}{-4}=\frac{8}{-4}\] =-2?
shubhamsrg
  • shubhamsrg
okay, vertex is (1,-2)
DLS
  • DLS
lol
shubhamsrg
  • shubhamsrg
focus would have been (1,0) if vertex had been (0,0)
DLS
  • DLS
oh...yeah
shubhamsrg
  • shubhamsrg
because of this shifting, new vertex = ?
DLS
  • DLS
so (1+a,-2)
shubhamsrg
  • shubhamsrg
i mean new focus= ?
DLS
  • DLS
!!!
shubhamsrg
  • shubhamsrg
shift (1,0) 1 unit to the right and 2 units down
DLS
  • DLS
2,-2 right?
shubhamsrg
  • shubhamsrg
yep,
DLS
  • DLS
that's what i wrote earlier :P
DLS
  • DLS
(1+a,-2) a=1
shubhamsrg
  • shubhamsrg
now you have eqn of line PQ
shubhamsrg
  • shubhamsrg
find co-ordinate of Q
DLS
  • DLS
m=4
DLS
  • DLS
slope of line PQ=4
shubhamsrg
  • shubhamsrg
noooo.....
DLS
  • DLS
:o
DLS
  • DLS
\[y-2=m(x+3)\]
DLS
  • DLS
-2-2=m(-1) m=4
shubhamsrg
  • shubhamsrg
P(-3,2) F(2,-2) slope = -4/5
DLS
  • DLS
:|
shubhamsrg
  • shubhamsrg
x=2 and not -2
DLS
  • DLS
oh :p
shubhamsrg
  • shubhamsrg
so slope = -4/5 eqn of line = ?
DLS
  • DLS
5y+4x+2=0
shubhamsrg
  • shubhamsrg
okay.
shubhamsrg
  • shubhamsrg
eqn of parabola = y^2 + 4x+ 4y =0 eqn of line = 5y + 4x + 2 =0 solve both to solve for Q
DLS
  • DLS
oh pellet :|
shubhamsrg
  • shubhamsrg
Note that you'll obtain 2 solutions from here, 1 should easily be (-3,2)
shubhamsrg
  • shubhamsrg
So its easy, form a quadratic, use sum of roots thing, you already know (-3,2) is a solution, just find other co-ordinate
DLS
  • DLS
abe yaar short method bata :P i took the wrong road nvm
shubhamsrg
  • shubhamsrg
Arey ho to gaya hai, bas Q nikalna hai,
DLS
  • DLS
why are we solving both the equations together? Q doesn't lie on parabola does it?
shubhamsrg
  • shubhamsrg
Ofcorse it does! PQ is the focal chord
DLS
  • DLS
but P doesn't lie on parabola?
shubhamsrg
  • shubhamsrg
Of course it does, what are you saying!
DLS
  • DLS
check it
shubhamsrg
  • shubhamsrg
Just did,
shubhamsrg
  • shubhamsrg
(y+2)^2 = 4(1-x)
shubhamsrg
  • shubhamsrg
x=-3 and y=2
DLS
  • DLS
but logically when I saw.. Vertex=(-1,2) P=(-3,2) how big is the parabola :X
shubhamsrg
  • shubhamsrg
vertex = (1,-2)
DLS
  • DLS
wahi wahi
shubhamsrg
  • shubhamsrg
are you sleep deprived? o.O
DLS
  • DLS
:/
shubhamsrg
  • shubhamsrg
I don;t understand your query
DLS
  • DLS
|dw:1359795719275:dw| how does it lie on the parabola? forget the substi. method for a while
shubhamsrg
  • shubhamsrg
|dw:1359795779003:dw|
DLS
  • DLS
:O
DLS
  • DLS
that would happen if \[\LARGE y^2=-4ax\]
DLS
  • DLS
oh wahi to hai NVM
DLS
  • DLS
sorry :/
shubhamsrg
  • shubhamsrg
hmm.
shubhamsrg
  • shubhamsrg
I minded! :|
DLS
  • DLS
sleep deprived :P
shubhamsrg
  • shubhamsrg
So, shall we find Q now ?
DLS
  • DLS
finding
shubhamsrg
  • shubhamsrg
just forma quad, rest is easy
shubhamsrg
  • shubhamsrg
y^2 + 4x+ 4y =0 5y + 4x + 2 =0 =>4x = -5y -2 make that substitution
DLS
  • DLS
\[\LARGE y^2-y-2=0\]
shubhamsrg
  • shubhamsrg
Okay, one root of this is 2,right ?
DLS
  • DLS
yeah!
shubhamsrg
  • shubhamsrg
use sum of roots or any other legit method, find other root.
DLS
  • DLS
-1
shubhamsrg
  • shubhamsrg
okay, so x=?
DLS
  • DLS
1?
shubhamsrg
  • shubhamsrg
x= -5y-2
shubhamsrg
  • shubhamsrg
y=-1
DLS
  • DLS
oh yeah wahi :P
shubhamsrg
  • shubhamsrg
i mean 4x= -5y-2
DLS
  • DLS
3/4
shubhamsrg
  • shubhamsrg
Q(3,4 ,-1)
DLS
  • DLS
3/4*
shubhamsrg
  • shubhamsrg
actually we needn;t find x,
shubhamsrg
  • shubhamsrg
slope of normal = (2y+4)/4
DLS
  • DLS
how?
shubhamsrg
  • shubhamsrg
tumhi ne to upar differentiate karke nikala tha
DLS
  • DLS
i dont want to live on this planet anymore
DLS
  • DLS
why did we do all this then?
shubhamsrg
  • shubhamsrg
We had to find y co-ordinate of Q
DLS
  • DLS
oo I SEE
shubhamsrg
  • shubhamsrg
So ans ?
DLS
  • DLS
wait :o
DLS
  • DLS
-4 hai ya +4?
shubhamsrg
  • shubhamsrg
tum batao.
DLS
  • DLS
\[\LARGE \frac{2y+4}{-4}\]
shubhamsrg
  • shubhamsrg
-4/(2y+4) ye tangent ka hai, right?
DLS
  • DLS
yeah
shubhamsrg
  • shubhamsrg
slope of tangent * slope of normal = -1
DLS
  • DLS
oh..okay
DLS
  • DLS
so 1/2?
shubhamsrg
  • shubhamsrg
abhi bhi confidence nahi aya?
DLS
  • DLS
1/2.
shubhamsrg
  • shubhamsrg
B|
DLS
  • DLS
dont say -1/2 dil tut jaega :'(
shubhamsrg
  • shubhamsrg
okay, nahi kahunga
DLS
  • DLS
answer to wahi hai be :P -1/2
shubhamsrg
  • shubhamsrg
na, ans 1/2 hoga.
DLS
  • DLS
-1/2 IIT q tha ye
shubhamsrg
  • shubhamsrg
leme check.
DLS
  • DLS
http://www.goiit.com/posts/list/geometry-simple-parabola-question-14790.htm
DLS
  • DLS
Solution(A)
shubhamsrg
  • shubhamsrg
usme kya uqes hai aur tumne kya copy kiya hai! :3
shubhamsrg
  • shubhamsrg
ques*
DLS
  • DLS
O_o usme ques kya hai ?
shubhamsrg
  • shubhamsrg
parabola ka eqn dekho
DLS
  • DLS
-1/2 in my register
shubhamsrg
  • shubhamsrg
abe parabola ka eqn dekho
DLS
  • DLS
mine is correct :|
shubhamsrg
  • shubhamsrg
y^2 + 4x + 4y =0 tumne likha hai y^2 + 4x + 4 =0 hai
DLS
  • DLS
\[\LARGE \frac{-4}{4+4}\] that s what i got in last in register
DLS
  • DLS
myequation is right!! 101% ques might be different..
DLS
  • DLS
issi Q ke hisb se -1/2 aya hai
shubhamsrg
  • shubhamsrg
ha, uska ans -1/2 hoga, lekin iska 1/2 hai.
DLS
  • DLS
iska -1/2 hai
shubhamsrg
  • shubhamsrg
kon se saal ka hai ?
DLS
  • DLS
no idea,disha me nahi hai
shubhamsrg
  • shubhamsrg
1/2 hai iska.
shubhamsrg
  • shubhamsrg
-1/2 uska hoga.
DLS
  • DLS
IDK..its -1/2..chod
shubhamsrg
  • shubhamsrg
mujhe to nahi lag raha abhi tak kahi koi galti ki hai ?
shubhamsrg
  • shubhamsrg
ohh. ::O
shubhamsrg
  • shubhamsrg
focus !
DLS
  • DLS
o.o
DLS
  • DLS
focus?
shubhamsrg
  • shubhamsrg
(y+2)^2 = 4(-1)((x-1) vertex = (1,-2) focus was (-1,0) for vertex (0,0) so new focus will be (0,-2)
shubhamsrg
  • shubhamsrg
eqn of line = (y-2) = m(x+3)
shubhamsrg
  • shubhamsrg
m= -4/3
DLS
  • DLS
http://www.theparentingdad.com/wp-content/uploads/2012/08/baby-facepalm.jpg
DLS
  • DLS
wait i didnt get the focus thing :/
DLS
  • DLS
kya kiya tune usme?
shubhamsrg
  • shubhamsrg
focus (-1,0) hoga y^2 = -4ax me
shubhamsrg
  • shubhamsrg
ham (1,0) like kar rahe the
shubhamsrg
  • shubhamsrg
3y + 4x +6 =0
shubhamsrg
  • shubhamsrg
y^2 + 4x + 4y =0 and 4x = -6-3y => y^2 + y -6 =0 1 ans hai 2, dusra ho jayega -3
shubhamsrg
  • shubhamsrg
ab slope of normal = 4/(2y+4) = -2 hahahha
DLS
  • DLS
lol o.o
DLS
  • DLS
par kya hai ke na focus wala part smaj nahi aya :P
shubhamsrg
  • shubhamsrg
ye ques repost karo firse, koi expert batayega, ise close kar do
DLS
  • DLS
do we have a greater expert than you ?:P
shubhamsrg
  • shubhamsrg
wo to dikh gaya, :3
DLS
  • DLS
BOLNA dhang se focus wala bus :'(
shubhamsrg
  • shubhamsrg
y^2 = -4ax ke type ka hai hamara eqn
DLS
  • DLS
yo
shubhamsrg
  • shubhamsrg
waha focus (-1,) hota hai jab vertex (0,0) hota hai.
shubhamsrg
  • shubhamsrg
yaha vertex (1,-2) hai
DLS
  • DLS
OH :o
shubhamsrg
  • shubhamsrg
to focus (-1+1 , 0-2) = (0,-2)
DLS
  • DLS
:D
DLS
  • DLS
m=0 aa raha hai ?
DLS
  • DLS
damwait
shubhamsrg
  • shubhamsrg
wait wait, -1/2 aa to raha hai!
shubhamsrg
  • shubhamsrg
yeah !
DLS
  • DLS
m=-4/3
DLS
  • DLS
wtf :/
DLS
  • DLS
3y+4x+6=0!!!
shubhamsrg
  • shubhamsrg
(2y+4)/4 y=-3 slope = -1/2
shubhamsrg
  • shubhamsrg
last me thora pagla gaya tha mai, ho to gaya, 1-/2
shubhamsrg
  • shubhamsrg
-1/2*
DLS
  • DLS
"nahi hamara answer sahi hai :p "
shubhamsrg
  • shubhamsrg
focus toot gaya tha! :|
DLS
  • DLS
mai kar raha hoon dubara bus hogaya..1m..BC 1 ghanta hogya :/
shubhamsrg
  • shubhamsrg
hmm..
shubhamsrg
  • shubhamsrg
ja raha hu, bye
DLS
  • DLS
y=3 hai?
shubhamsrg
  • shubhamsrg
-3
DLS
  • DLS
yeah wahi :P
DLS
  • DLS
OMG AAGAYA O____O
DLS
  • DLS
ahaaa maza agaya :P mast Q :P
shubhamsrg
  • shubhamsrg
aasan tha! :|
DLS
  • DLS
yeah :o
DLS
  • DLS
chal lunch:P thanda hogaya :/
shubhamsrg
  • shubhamsrg
bye

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