The locus of the centres of the circles, which touch the circle, x2
+ y2
= 1 externally, also touch the y-axis and
lie in the first quadrant, is :
Solutions · 1
Official solution
Let the centre is (h, k) \& radius is h (h, k > 0)
OP = h + 1
\[\sqrt {{h^2} + {k^2}} = h + 1\]
\[ \Rightarrow {h^2} + {k^2} = {h^2} + 2h + 1\]
\[ \Rightarrow {k^2} = 2h + 1\]
\[ \therefore \] Locus is y2 = 2x + 1