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 The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on :


  • Option 1)

     a circle.


  • Option 2)

    an ellipse which is not a circle.


  • Option 3)

     a hyperbola.


  • Option 4)

     a parabola.


Answers (2)


As we learnt in

Common tangents of two circles -

When two circles touch  each other externally, there are three common tangents, two of them are direct.


- wherein



Circle touching x-axis and having radius r -

x^{2}+y^{2}\pm 2rx+2fy+f^{2}= 0

- wherein

Where f is a variable parameter.



Standard equation of parabola -


- wherein


 Circle: x^{2}+y^{2}-8x-8y-4=0


radius of circle touching x-axis=k,

we get C_{1}C_{2}=\sqrt{(h-4)^{2}+(k-4)^{2}}=k+6

On squaring both sides



\left ( h-4 \right )^2=16\left ( k+\frac{5}{4} \right )

compared to x^{2}=4AY

Represent a parabola

Option 1)

 a circle.


Incorrect Option

Option 2)

an ellipse which is not a circle.


Incorrect Option

Option 3)

 a hyperbola.


Incorrect Option

Option 4)

 a parabola.

Correct option

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