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Analytical Geometry

Blazing goIITian

Joined:	1 Jan 2008
Post:	794

17 Apr 2008 21:38:31 IST

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514

ellipse doubt.....

None

1)if centre at (2,-3)

focus at (3,-3)

and vertex at (4,-3) thn eqn of ellipse is?????

guys actuallly i wnt any shortcut for this some.

if not thn how will u solve this sum if it comes in any competitive exam?

2) for d ellipse 5x^2 + 9y^2 + 10x - 36y -4 = 0 the foci are ???

shortcut for this too if any.

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Comments (8)

srk

Blazing goIITian

Joined: 1 Jan 2008

Posts: 794

18 Apr 2008 09:04:55 IST

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chalo reply karo goiitians

iitaspirant10

Blazing goIITian

Joined: 16 Dec 2006

Posts: 424

18 Apr 2008 09:49:02 IST

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Sagar Vaze

Blazing goIITian

Joined: 11 Apr 2008

Posts: 315

18 Apr 2008 10:17:07 IST

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shift origin to 2.-3
X=x-2 Y=y+3
in new system focus ( 1,0)
vertex ( 2,0)
now focus at ae from centre and vertex at a
so e=0.5 and a=2
so b^2=a^2(1-e^2) = 4*(3/4) =3
so eqn is X^2/4+Y^2/3=1
no substiture X=x-2 Y=y+3

so (x-2)^2/4+(y+3)^2/3=1

srk

Blazing goIITian

Joined: 1 Jan 2008

Posts: 794

18 Apr 2008 15:24:52 IST

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nice work sagar
but wht about mine second question?

chemicaltester

Scorching goIITian

Joined: 12 Mar 2008

Posts: 233

18 Apr 2008 23:51:39 IST

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i cannot solve complete problem cos it is too lengthy to write
but use shift of origin in such way that the vertex comes at the new origin in that then find focii using focus is(+- ae ,o)

Brad

Moderator

Joined: 9 Sep 2007

Posts: 647

19 Apr 2008 07:09:56 IST

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5x² + 9y² + 10 x - 36y - 4 = 0

5 [ x² + 2 x + 1 ] + 9 [ y² - 4y + 4 ] = 45

or (x+1)² / 9 + (y - 2)² / 5 = 1

X²/a² + Y²/b² = 1

e =

(1 - 5/9) = 2/3

So now , X = 0 , Y =

ae

So x + 1 = 0 , y - 2 =

6

So foci = ( -1, 8 ) , ( - 1 , - 4 )

Sorry if there are calculation mistakes

srinath

Scorching goIITian

Joined: 24 Jan 2008

Posts: 266

19 Apr 2008 08:51:40 IST

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GREAT DREAMS ,please check ur nudge book , sorry 4 the interruption guys.

srk

Blazing goIITian

Joined: 1 Jan 2008

Posts: 794

21 Apr 2008 10:07:14 IST

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guys is thier any other way to find foci ????

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