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Analytical Geometry

Cool goIITian

Joined:	27 Apr 2009
Post:	60

1 Oct 2009 18:01:12 IST

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Find the shortest distance between the curves y^2=4x and x^2+y^2-24y+128=0 Someone please help

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Find the shortest distance between the curves y^2=4x and x^2+y^2-24y+128=0Someone please help

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C!-!!NMAY

Blazing goIITian

Joined: 30 Mar 2008

Posts: 1415

1 Oct 2009 18:06:02 IST

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wait posting solution

C!-!!NMAY

Blazing goIITian

Joined: 30 Mar 2008

Posts: 1415

1 Oct 2009 18:10:00 IST

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see shortest distance between any two curve is along their common normal....

we have y^2=4x.

....and x^2+y^2-24y+128=0.....

eqn of normal of parabola is

y=mx-2am-am^3...................(1)here a=1

as this line is also normal to circle ,,,,and normal of circle will pass thru its centre ,,,,,

centre of circle is (0,12)

now it will satisfy (1),,,u will get

am^3+2am+12=0...from here u will get m,,,and then eqn,,,,

then solve eqn wid circle and parabola,,,,

and then find shortest distance b/w them by applying distance formula

hope i helped u....

sharath

Cool goIITian

Joined: 26 Oct 2009

Posts: 80

25 Feb 2010 16:13:24 IST

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what if the other figure was not a circle

Sarthak Verma

Hot goIITian

Joined: 15 Nov 2009

Posts: 118

25 Feb 2010 16:49:14 IST

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then write equation of nomal for the second curve also, then compare their coefficients since both the equations represent the same line...

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