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The locus of the centre of a circle which touches the circle | z – z1 | = a and | z – z2 | = b externally (z , z1 & z2 are complex numbers) will be [2002]
  • a)
    an ellipse
  • b)
    a hyperbola
  • c)
    a circle
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The locus of the centre of a circle which touches the circle | z &ndas...
(b) Let the circle be |z – z0| = r. Then according to given conditions |z0 – z1| = r + a and |z0 – z2|= r + b.
Eliminating r, we get |z0 – z1| –|z0 – z2| = a – b.
∴ Locus of centre z0 is |z – z1| –|z – z2| = a – b,
which represents a hyperbola.
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Most Upvoted Answer
The locus of the centre of a circle which touches the circle | z &ndas...
- a | = r, where a is a complex number and r is a positive real number, is a circle with center -a and radius r.
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