Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes. ( Give your answer as a whole or exact number.)

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

The numerical value of the slope is:

The component of the y-axis is:

Now, the tangent line has the following mathematical model:

The value of the intercept is found by isolating it within the equation and replacing all known variables:

Thus, the tangent line is:

The vertical distance between a point of the tangent line and the origin is given by the intercept.

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

The area of the triangle is computed by this formula:

step-by-step explanation: