Area of a Triangle from a Tangent Line to an Ellipse

On the rectangular coordinate plane, an ellipse with equation $4x^2 + y^2 = 64$ is given. A line $L$ with slope 2 is tangent to the ellipse at a point on the ellipse in the second quadrant. What is the area of the triangle bounded by the $x$-axis, the $y$-axis, and line $L$?