Question

A circle is given by x^2 + (y-1)^2 =1 . Another circle C touches it externally and also the x-axis then the locus of its center is​

Answer 1

Answer:

Let centre of circle C be (h, k)

Circle touches x–axis. Hence radius = |k|

also it touches circle x2 + (y – 1)2 = 1

Where centre (0, 1) and radius is 1 externally.

∴ Distance between centre = sum of radii

∴ √[(h – 0)2 + (k – 1)2] = 1 + |k|

∴ h2 + k2 – 2k + 1 = 1 + 2(k) + k2

∴ h2 = 2k + 2|k|

locus of (h, k) x2 = 2y + 21y

Now if y > 0, it becomes x2 = 4y

if y < 0, then x = 0

∴ locus is {(x, y) : x2 = 4y} {(0, y) : y = 0}

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Answer 2

Answer:

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