Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

The equation of the line tangent to the hyperbola at the point is .

By analytical geometry we know that tangent lines are described by the line equation:

(1)

Where:

By calculus we know that the slope of the tangent line is defined by the first derivative of the hyperbola evaluated at point of tangence:

(2)

If we know that and , then the equation of the tangent line is:

The equation of the line tangent to the hyperbola at the point is .

To learn more on tangent lines, we kindly invite to check this verified question: link

on a coordinate grid, point a is at (−4.0, −2.4) and point b is at (4.0, −2.4). point b is a reflection of point a across the –axis. input either a lowercase x or i think is the right awnser

step-by-step explanation: