SOLUTION: i have to write an equation of the line that is tangent to the circle at that point: x^2+y^2=50; (-7,1)

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Question 194785: i have to write an equation of the line that is tangent to the circle at that point:
x^2+y^2=50; (-7,1)
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
i have to write an equation of the line that is tangent to the circle at that point:
x^2+y^2=50; (-7,1)

Find the derivative by the method of implicit functions











Substitute (x,y)=(-7,1)





Therefore the slope, m, of the tangent line
at (-7,1) is 7.  So m=7

Now we use the point-slope form of the
equation of a line:











To check it we draw the equation of the circle
and the line:



Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
First, answer the question: "Is the point (-7,1)
on the circle?"



Yes
The center of the circle is the origin.
Next find the equation of the line that
contains the points (0,0) and (-7,1)


Multiply both sides by




This is of the form , and is the slope
Any line perpendicular to this one will have slope
, in this case,
So, the line tangent to the circle at (-7,1) will have
slope = .



answer
I'll plot the circle and the line
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