JEE-Mains 2015 (20/30)

Geometry Level 3

{ x 2 + y 2 − 4 x − 6 y − 12 = 0 x 2 + y 2 + 6 x + 18 y + 26 = 0 \begin{cases} x^2+y^2-4x-6y-12=0 \\ x^2+y^2+6x+18y+26=0 \end{cases}
The number of common tangents to the above two circles is :

1 2 4 3

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Prakhar Bindal
Jun 15, 2015

Comparing The Equations With Standard form of circle we get centers of the circles are (2,3) and (-3,-9) respectively . also the radius are 5 and 8 respectively On Little bit observation we get distance between centers using distance formula = 13 units = sum of radii (5+8) So that means the circle touch each other externally. so there will be two direct common tangents and one other tangent passing through the point where the circle touch each other

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