Statement–1 : An equation of a common tangent

Question:

Statement-1 : An equation of a common tangent to the parabola $y^{2}=16 \sqrt{3} x$ and the ellipse $2 x^{2}+y^{2}=4$ is $y=2 x+2 \sqrt{3}$

Statement-2 : If the line $y=m x+\frac{4 \sqrt{3}}{m},(m \neq 0)$ is a common tangent to the parabola $y^{2}$ $16 \sqrt{3} \mathrm{x}$ and the ellipse $2 \mathrm{x}^{2}+\mathrm{y}^{2}=4$, then $\mathrm{m}$ satisfies $\mathrm{m}^{4}+2 \mathrm{~m}^{2}=24$

  1. Statement–1 : An equation of a common tangent

  2.  Statement–1 is false, Statement–2 is true.

  3.  Statement–1 is true, Statement–2 is true ; Statement–2 is a correct explanation for

         Statement–1.

  4.  Statement–1 is true, Statement–2 is true ; Statement–2 is not a correct explanation for

        Statement– 1.


Correct Option: , 3

Solution:

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