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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

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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... read more

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.

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Centre of first Circle is A(0,0) and second centre is B(3,4). So distance between centres is 5. Radius of first circle=x=2 and radius of second y=7 So AB=|x-y|. So circles touch internally. Hence only one common tangent.

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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... read more

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... read more

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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