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  • Let  be a common tangent line to the curves   <img alt="\mathrm {9 x^2+16 y^2=144}" src="ht

Let \mathrm L be a common tangent line to the curves   \mathrm {9 x^2+16 y^2=144}   and   \mathrm {x^2+y^2=15} . Then the square of the slope of the line  \mathrm L  is

Option: 1

5


Option: 2

6


Option: 3

7


Option: 4

1


Answers (1)

best_answer

Given curves are  \mathrm {\frac{x^2}{16}+\frac{y^2}{9}=1 }   and  \mathrm {x^2+y^2=15 } 
Let slope of common tangent be \mathrm {m }
So, tangents of given ellipse and circle are respectively


\mathrm { y=m x \pm \sqrt{16 m^2+9} \text { and } y=m x \pm \sqrt{15} \sqrt{1+m^2} }
Hence,

\mathrm { 16 m^2+9=15\left(1+m^2\right) \Rightarrow 16 m^2+9=15+15 m^2 \Rightarrow m^2=6 }

Posted by

himanshu.meshram

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