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Analytical Geometry

Blazing goIITian

Joined:	2 Jun 2007
Post:	465

17 Jan 2009 22:29:34 IST

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1475

3 excellent ellipse questions

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Analytical Geometry

1.consider the ellipse 4(x+y-5)^2+9(x-y+9)^2=36 then which of the following about its focci are correct:

a.both of them lie in third quadrant

b.both of them are in second quadrant

c.one lies in third quadrant and another in first

d.one lise in second and another in first

2.an ellipse of major axis 20 root 3 and mnor axis 20 slides along the co ordinate axes always remains confined in first quadrant .locus of centre of ellipse therefore describes the arc of a circle .the length of the arc is :

a.5 pi b.20pi c.5pi/3d. 20 pi/3

Comments (4)

kabi

Blazing goIITian

Joined: 11 Jan 2009

Posts: 575

17 Jan 2009 23:04:33 IST

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hello

1.(x+y-5)=0 and x-y+9=0 are perpendicular to each other.

put X=x+y-5/sqrt(2) Y=x-y+9/sqrt(2)

thus ur equation now is :

4X² + 9Y²=9

4X^2/9 +y^2=1

a²=9/4 b²=1 e=sqrt(5)/3

centre =(0,0) focus =(-+sqrt(5)/4,0)

in original centre would be (-2,7)

and for focus

we x+y-5=+-sqrt(5)/4

x+y+9=0

thus x=+-sqrt(5)-16/8 both are negative corresponding y value is positive .

thus b is the answer.

hey buddy I m really tired so if I have done some calculation mistake kindly correct me.

thank u

kabi.

debmalya choudhuri

Blazing goIITian

Joined: 2 Jun 2007

Posts: 465

18 Jan 2009 21:27:41 IST

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wat abt the second one?

ookie

New kid on the Block

Joined: 12 May 2012

Posts: 3

12 May 2012 18:38:01 IST

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5 pi/3 ??????????????????

Himanshu trehan

New kid on the Block

Joined: 7 Jan 2013

Posts: 1

7 Jan 2013 18:19:53 IST

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wat abt 2nd one yr??? i need ans..

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