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Solve it, Two circles with equal radii intersecting at the points (0,1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle.Then the distance between the centres of these circles is:

Two circles with equal radii intersecting at the points (0,1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle.Then the distance between the centres of these circles is:

  • Option 1)

     

    2

  • Option 2)

     

    2\sqrt2

  • Option 3)

     

    \sqrt2

  • Option 4)

     

    1

Answers (1)
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A admin

 

Orthogonality of two circle -

Two circles S_{1}=0 and S_{2}=0  are said to be orthogonal ,if tangents at their point of intersection include right angle.

 

- wherein

2g_{1}g_{2}+2f_{1}f_{2}=c_{1}c_{2}

 

Let centre of circle are \left ( c,0 \right ) &  \left ( -c,0 \right )

\Rightarrow equation of circles are 

\left ( x-1 \right )^{2}+\left ( y-0 \right )^{2}=c^{2}+1

and 

\left ( x+1 \right )^{2}+\left ( y-0 \right )^{2}=c^{2}+1

\Rightarrow since circles are orthogonal so , 

2\left ( c \right )\left ( -c \right )+\left ( 0 \right )\left ( 0 \right )=\left ( -1 \right )+\left ( -1 \right )

\Rightarrow c^{2}=1\Rightarrow c=\pm 1

Distance between \left ( -1,0 \right ) &  \left ( 1,0 \right ) is 2

 


Option 1)

 

2

Option 2)

 

2\sqrt2

Option 3)

 

\sqrt2

Option 4)

 

1

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