SOLUTION: Find the equation of the tangent to {{{y=1/(x-4)}}} that passes through the origin.

Algebra.Com
Question 1151169: Find the equation of the tangent to that passes through the origin.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


An arbitrary point on the graph of the function is (a,1/(a-4)).

We need to have the slope of the line containing (0,0) and (a,1/(a-4) equal to the slope of the graph of y=1/(x-4) at x=a -- that is, equal to the derivative of the function at x=a.




The derivative at x=a is



The slope of the line containing (0,0) and (a,1/(a-4) is



So







or

The function is undefined at x=4; so our solution should be at x=2.

For x=2, the point on the graph is (2,1/(2-4)) = (2,-1/2).

The line through (0,0) and (2,-1/2) -- and therefore the tangent line we are looking for -- is y = (-1/4)x.

A graph of the function and the tangent line through the origin:




RELATED QUESTIONS

Find the equation of the tangent to the curve y = e^x which passes through the origin... (answered by stanbon)
Find the equation of the circle that passes through the origin and (2,4); tangent to the... (answered by josgarithmetic,ikleyn)
9.Find the equation of a circle with center (1, -1) and that passes through the origin. (answered by stanbon)
Use the equation y=a*(x+4)^2+2 to find the equation whose curve passes through the... (answered by LinnW)
Find the equation of the line that is parallel to and that passes through the... (answered by Alan3354)
Find the equation of the line that passes through point (0,5) and is tangent to the curve (answered by fractalier)
Find the Equation of the line that passes through point (0,5) and is tangent to the curve (answered by stanbon)
Find the equation of the line that passes through point (0,5) and is tangent to the curve (answered by Edwin McCravy)
Find an equation of the line that passes through the origin and is perpendicular to the... (answered by Alan3354)