Question

find the equation for the tangent line to the curve y=4/x at the point (4,1) on this curve?

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Answer 1

Answer:x+4y-8=0

Step-by-step explanation:

y'=-4/x^2=-4/4^2=-1/4

m=-1/4

Using slope point form,

(y-1)=-1/4(x-4)

4y-4=4-x

x+4y-8=0

Alternative method:-

y=4/x

xy=4

This is inclined hyperbola.

xy=c^2

So c=2

For this hypernola,

Eqn of tang at x1,y1 is

x/x1 + y/y1 =2

So,

x/4 + y/1=2

x+4y-8=0