If m is the slope of a common tangent to the curves x^216+y^29=1 and x^2+y^2=12, then 12m^…

Question

If $m$ is the slope of a common tangent to the curves $\dfrac{x^2}{16}+\dfrac{y^2}9=1$ and $x^2+y^2=12$, then $12m^2$ is equal to:

Accepted Answer

Tangent to circle radius $\sqrt{12}$: $16m^2+9=12(1+m^2)\Rightarrow4m^2=3\Rightarrow m^2=\dfrac34$.

$12m^2=9.$

Solutions · 1