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The locus of the centre of a circle,whic...

The locus of the centre of a circle,which touches the circles`|z-z_1|=a` and `|z-z_2|=b` externally can be

A

an ellipse

B

a hyperbola

C

a circle

D

parabola

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Knowledge Check

  • The locus of centre of the circle which touches the circle x^(2)+(y-1)^(2)=1 externally and also touches x-axis is

    A
    `{(x, y):x^(2)+(y-1)^(2)=4} cup {(x,y): y lt 0}`
    B
    `{(x,y):x^(2)=4y} cup {(0, y) : y lt 0}`
    C
    `{(x,y) :x^(2) =y} cup {(0, y) : y lt 0}`
    D
    `{(x,y):x^(2)=4y} cup {(x,y) : y gt 0}`
  • The locus of centre of the circle which touches the circle x^(2)+(y-1)^(2)=1 externally and also touches x-axis is

    A
    `{(x, y):x^(2)+(y-1)^(2)=4} cup {(x,y): y gt 0}`
    B
    `{(x,y):x^(2)=4y} cup {(0, y) : (y lt 0)}`
    C
    `{(x,y):x^(2)=y}cup {(0,y): y lt 0}`
    D
    `{(x,y):x^(2)=4y} cup {(x,y) : y lt 0}`
  • The locus of the centre of a circle the touches the given circle externally is a _______

    A
    curve
    B
    straight line
    C
    circle
    D
    helix
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