Form the intersection point of the circle $x^2+y^2=9$ and the line $y=2x$ perpendicular is drawn to the major axis of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1,$ which meets the ellipse at point M,  then equation of tangent at M to the ellipse can be 

Intersection point of circle $x^2+y^2=9$ and line $y=2x$ will be $(\frac{3}{\sqrt{5}},\frac{6}{\sqrt{5}})$ and $(\frac{3}{\sqrt{5}},\frac{6}{\sqrt{5}})$ Coordinates of the point of intersection of perpendicular drawn from these points to the major 
Axis of ellipse and ellipse will be $(\frac{3}{\sqrt{5}},-\frac{4}{\sqrt{5}}), (\frac{3}{\sqrt{5}},-\frac{4}{\sqrt{5}}),(-\frac{3}{\sqrt{5}},\frac{4}{\sqrt{5}}),(-\frac{3}{\sqrt{5}}-\frac{4}{\sqrt{5}})$
Equation of tangents of these points will be $x+3y-3\sqrt{5}=0,x-3y-3\sqrt{5}=0$
$x-3y+3\sqrt{5}=0,and\text{\hspace{0.17em}\hspace{0.17em}}x+3y+3\sqrt{5}=0$