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Analytical Geometry

Blazing goIITian

 Joined: 2 Jun 2007 Post: 465
17 Jan 2009 22:29:34 IST
0 People liked this
4
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

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

or

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 .

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

thank u

kabi.

Blazing goIITian

Joined: 2 Jun 2007
Posts: 465
18 Jan 2009 21:27:41 IST
0 people liked this

wat abt the second one?

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 ??????????????????

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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