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

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.

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N

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 -

- wherein

Where f is a variable parameter.

Standard equation of parabola -

- wherein Circle:

externally

radius of circle touching x-axis=k, we get

On squaring both sides

compared to

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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