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Analytical Geometry

Cool goIITian

Joined:	7 Apr 2009
Post:	35

8 May 2010 10:18:43 IST

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Find the values of x; y for which x^2 + y^2 takes the minimum value where (x + 5)^2 + (y-12)^2 = 14

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Find the values of x; y for which x^2 + y^2 takes the minimum valuewhere (x + 5)^2 + (y-12)^2 = 14^2.

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Sujit

Blazing goIITian

Joined: 11 Mar 2009

Posts: 1345

8 May 2010 10:34:56 IST

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the x,y lie on the below circle with centre A(-5,12)

x²+y² implies distance of any point on the circle from the origin

for distance to be minimum the point should lie on the normal of the circle which passes through origin

as radius is 14 and distance between centre and origin is 13

thus minimum value of x²+y²=1

Deepak Aggarwal

Blazing goIITian

Joined: 9 May 2009

Posts: 766

8 May 2010 17:59:00 IST

Like 6 people liked this

Using triangular inequality,

So, minimum ( x² + y² ) = 1

Solving the equaitons now, you'll get

x = 5 / 13 and y = - 12 / 13

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