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The locus of the centre of circles touching the y-axis and circle x^2 + y^2 -2x=0 externally is

The locus of the centre of circles touching the y-axis and circle x^2 + y^2 -2x=0 externally is

Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
let the centre of such a circle be (h, k). as it touches the y axis, its radius will be h.
x^2 + y^2 -2x=0 has a radius of 1 and its center is on (1, 0).
now, as both circles touch, the distance between their centres will be the sum of their radii, ie, h+1.
the distance can also be writen as root( (k-0)^2+(h-1)^2 )
so, h+1= root( (k-0)^2+(h-1)^2 )
or h^2+2h+1=k^2+h^2-2h+1
or k^2=4h
changing h and k into x and y respectively
y^2=4x is the reqd locus

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