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Question

The locus of the centre of circle which touches (y1)2+x2=1 externally and also touches x-axis, is

A
{x2=4y,y0}{(0,y),y<0}
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B
x2=y
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C
y=4x2
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D
y2=4x(0,y),yϵR
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Solution

The correct option is A {x2=4y,y0}{(0,y),y<0}
Let the locus of centre of circle be (h, k) touching (y1)2+x2=1 and X- axis shown as


Clearly, from figure,
Distance between C and A is always 1+|k|,
i.e.(h0)2+(k1)2=1+|k|
h2+k22k+1=1+k2+2|k|h2=2|k|+2kx2=2|y|+2y
where |y|={y,y0y,y<0
x2=2y+2y,y0
and x2=2y+2y,y<0
x2=4y, when y0
and x2=0, when y<0
{(x,y):x2=4y, when y0}{(0,y);y<0}

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