What is the tangent of y= 2/((x-2)) ?

The tangent of y= 2/((x-2)) is y=-2/((a_{0)-2)^2}x+(4a_{0}-4)/((a_{0)-2)^2}

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tangent of y= 2/((x-2))

tangent of

y = \frac{2}{( x - 2 )}

y = - \frac{2}{( a _{0} - 2 ) ^{2}} x + \frac{4 a _{0} - 4}{( a _{0} - 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 2})

Find the slope of

y = \frac{2}{x - 2} : \frac{d y}{d x} = - \frac{2}{( x - 2 ) ^{2}}

Compute the slope of

y = \frac{2}{x - 2}

x = a_{0} : m = - \frac{2}{( a _{0} - 2 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 2 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 2}) : y = - \frac{2}{( a _{0} - 2 ) ^{2}} x + \frac{4 a _{0} - 4}{( a _{0} - 2 ) ^{2}}

y = - \frac{2}{( a _{0} - 2 ) ^{2}} x + \frac{4 a _{0} - 4}{( a _{0} - 2 ) ^{2}}

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What is the tangent of y= 2/((x-2)) ?
The tangent of y= 2/((x-2)) is y=-2/((a_{0)-2)^2}x+(4a_{0}-4)/((a_{0)-2)^2}