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How to find the no of common tangents to the circles x^2 + y^2 = 4 , x^2+y^2 -6x-8y =24
Asked by Diya Harish Last Modified
Answer 
Distance between centres = Sum of radii Three tangents. Two direct common tangent and one indirect common tangent.
Distance between centres Sum of radii
Two tangents. Two direct common tangents.
Distance between centres > Sum of radii Four tangents. Two direct common tangent and two indirect common tangents.
Ekaveera Kumar Gouribhatla
Tutor
Let R and r be the radii of the two circles. Find out the distance d between the centres of the circles. Then,
If d< abs(R-r), no common tangents
If d = abs(R-r), one common tangent
If abs(R-r) ≤ d ≤ max(R,r), two common tangents
If d = max(R,r), three tangents
If d > max(R,r), four tangents.
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First of all calculate the distance between centers of circle C (0,0) and C' (3,4) which is 5 units.By comparing general equation of circle, Radius of first circle is 2 unit and that of second is 7unit. As CC'=R-r, it means circles are touching internally. Hence, we can say that only one common tangent is possible.
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