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Let L be a common tangent line to the curves 4x2 + 9y2 = 36 and (2x)2 + (2y)2 = 31. Then the square of the slope of the line L is_____________
 

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detailed solution

3

Given : Ellipse is x29+y24=1

let tangent  be y=mx±9m2+4 It is tangent to the circle x2+y2=314then 9m2+4m2+1=312 4(9m2+4)=31(m2+1) 36m2-31m2=31-16 5m2=15 m2=3 


 

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