1
Question
The locus of the center of a circle which touches the circle
|z−z1|=a, |z−z2|=b externally will be
The locus of the center of a circle which touches the circle
|z−z1|=a, |z−z2|=b externally will be
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Solution
The correct option is B a hyperbola
Lets assume the circle which is touching both the circles externally has centre 'z0' and radius 'r'
∴ To find locus of 'z0'
we have conditions,
(1)---------|z0−z1|=a+r For the circle to touch (2)---------|z0−z2|=b+r other circle externally distance between centres = sum of radii .
Eliminating 'r' by subtracting the equations.
|z0−z1|−|z0−z2|=a−b
z0 is the centre of variable circle
∴|z−z1|−|z−z2|=a−b represents a hyperbola. Difference of distance from two fixed points is constant.
Lets assume the circle which is touching both the circles externally has centre 'z0' and radius 'r'
∴ To find locus of 'z0'
we have conditions,
(1)---------|z0−z1|=a+r For the circle to touch
(2)---------|z0−z2|=b+r other circle externally
distance between centres = sum of radii .
Eliminating 'r' by subtracting the equations.
|z0−z1|−|z0−z2|=a−b
z0 is the centre of variable circle
∴|z−z1|−|z−z2|=a−b represents a hyperbola. Difference of distance from two fixed points is constant.
Eliminating 'r' by subtracting the equations.
|z0−z1|−|z0−z2|=a−b
z0 is the centre of variable circle
∴|z−z1|−|z−z2|=a−b represents a hyperbola. Difference of distance from two fixed points is constant.
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