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Find the shortest distance from the line 3x + 4y = 25 to the circle x^2 + y^2 = 6x - 8y.

 Aug 16, 2021
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Using desmos, the circle you said will go through the point (6, 0). The shortest distance will be perpendicular to the line you said, and passes through the point (6, 0). Let's put the equation 3x + 4y = 25 into y = mx + b form. ==> 4y + 3x = 25 ==> 4y = -3x + 25 ==> y = (-3/4)x + 25/4. A line perpendicular it would have slope 4/3. Using point slope form, the equation perpendicular to 3x + 4y = 25 would be y - 0 = 4/3(x - 6) ===> y = (4/3)x - 8.  The point the equations y = (-3/4)x + 25/4 & y = (4/3)x - 8 will be (171/25, 28/25). The distance from (6, 0) to (171/25, 28/25) is 1.4. 

 

 

 

 

 

 

(ik this solution probably doesnt make sense)

 Aug 16, 2021

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