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Please Help with the following question.... It is a practice problem that I would like to solve:

 

 

Find the equation of a line tangent to the circle (x+1)^2+(y-4)^2=25 at the point (3, 1)

 

 

 

 

 

Appreciate you guys

Guest Sep 30, 2017
 #1
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The center of the circle is ( -1, 4 )

 

And the given point is ( 3, 1 )

 

Finding the slope between these two points, we have 

 

[  4 - 1 ] / [ -1 - 3]  =  [ 3] / [-4] =  -3/4

 

And the slope of the tangent ine will be the negative reciprocal of this   = 4/3

 

So.....the equation of the tangent line is :

 

y =  (4/3) (x - 3) + 1    simplify

 

y = (4/3)x - 4 + 1

 

y = (4/3)x - 3

 

Here's the graph : https://www.desmos.com/calculator/5u5jc97jd5

 

 

cool cool cool

CPhill  Sep 30, 2017
 #2
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CPhill, you are the best man

Guest Sep 30, 2017

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