# If the line y=mx+c is a common tangent to the hyperbola $\frac{x^2}{100}-\frac{y^2}{64}=1$ and the circle $x^2+y^2=36$ then which of the following is true? Option: 1 Option: 2 Option: 3 Option: 4

Equation of the circle $x^2+y^2=36$

Equation of a tangent to the circle $y=mx\pm6\sqrt{1+m^2}$

Equation of Hyperbola $y=mx\pm\sqrt{100m^2-64}$

For the common tangent

$\\36(1+m^2)=(100m^2-64)\\64m^2=100\\m^2=\frac{100}{64}\\Now, c=6\sqrt{1+m^2}=\\c^2=36(1+m^2)=\frac{369}{4}\\4c^2=369$

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