Q) A circle touches the x axis and also touches another fixed circle with center (0,3) and radius = 2 units. What is the locus of the center of the (first) circle?

A) Consider any such arbitrary circle, with center (h,k).

It touches the x axis, so its radius is k units ( the ordinate).

Now, the distance of this circle's center from the given circle's center = 2 + k units

This distance is the same as the distance between center of the arbitrary circle and the line y = -2 .

Now, since the center of this arbitrary circle is equidistant from a fixed point (the center of given circle ie. (0,3) ) and the line y = -2, it follows the definition of the parabola and hence the locus of (h,k) is a parabola.

So the locus of the center of the circle is a parabola with focus (0,3) and directrix y = -2 .

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## Saturday, December 13, 2008

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## 4 comments:

please help me

Q: How to find number of terms in the expansion

(1+x+x^2+x^3)^8

by a easier way or if their is a general formula please tell.....

please help me

Q: How to find number of terms in the expansion

(1+x+x^2+x^3)^8

by a easier way or if their is a general formula please tell.....

please help me

Q:How to find number of terms in the expansion (1+x+x^2+x^3) by an easier way or is their an easier way to find number of terms please help me...............

please help me

Q:How to find number of terms in the expansion (1+x+x^2+x^3) by an easier way or is their an easier way to find number of terms please help me...............

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