The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on :
a circle.
an ellipse which is not a circle.
a hyperbola.
a parabola.
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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