## 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

Question

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.)

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2 days 2021-10-11T15:39:33+00:00 1 Answer 0 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:   