[JEE Main 2002] the locus of the centre of a circle which touches z z 1 a
The locus of the centre of a circle which touches $|z-z_1|=a$ and $|z-z_2|=b$ externally is
(a) an ellipse
(b) a hyperbola
(c) a circle
(d) none of these
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (b) a hyperbola
If the moving centre is $P$ with radius $R$, $|P-z_1|=R+a$ and $|P-z_2|=R+b$, so $|P-z_1|-|P-z_2|=a-b$ (constant) — a hyperbola.
JEE Main 2002 · Complex Numbers — verified solution by the Vidaara Team.
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