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Analytical Geometry

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Joined:	6 Jan 2007
Post:	706

28 Jan 2007 20:53:42 IST

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626

Who can solve this Part-3

None

Sir plz help!

The locus of the centre of a circle which touches externally the given two circles is?

Ans is hyperbola.

I tried but couldn't get it.

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SUDEEP KUMAR

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Joined: 23 Jan 2007

Posts: 373

29 Jan 2007 16:18:12 IST

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I have seen ur posts Adarsh, and i think u can solve it..

i m just givin a hint...try it.. tell me if u still cant solve it.. i will post a complete solution.

Let the radius of the variable circle is r, and that of the two fixed circles is R₁ and R₂. Then, r moves in such a way that the difference of its distance from two fixed points, the two centres is equal to (R₁+ r) - (R₂ + r) = (R₁ - R₂)... which is a constant... so isnt it short of definiton of parabola..

(if the sum of dist from two pts is fixed, it is an ellipse.)

To prove it analytically... just try going along the same thought.

nrki99

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Joined: 20 Jan 2007

Posts: 122

29 Jan 2007 16:22:23 IST

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hi kab,

consider a circle with centre p(radius c) which touches the two circles externally with centres q&r (radius a&b) respectively.then

pq= c+a & pr= c+b

then pq-pr= a-b

pq-pr = constant

which is the locus of hyperbola

CyBorG

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Joined: 6 Jan 2007

Posts: 706

30 Jan 2007 09:16:29 IST

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It was quite an easy one.I had thought of proving it analytically and was stuck some where.Thanx.

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