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The circle (x + 3)2 + (y − 4)2 = 36 and the line 3x − 4y + 5 = 0 intersect twice as shown below. What is the greatest distance from a point on the circle to the line?

 May 22, 2021
 #1
avatar+121054 
+1

The  center of the circle =   (-3, 4)

 

Using   the formula  for the  distance  from a point to a line we have  that

 

l  3(-3)  - 4(4)  + 5  l              l  -20  l

________________    =     ________   =     20   / 5   =    4

    sqrt ( 3^2 + 4^2)              sqrt 25

 

Adding the radius  (6)  to  this gives us  the  greatest distance from  a point on the  circle to the line =   10

 

CORRECTED  !!!....thx  Shibu   !!!

 

 

cool cool cool

 May 22, 2021
edited by CPhill  May 25, 2021
 #2
avatar+12 
0

just a little typo but 20/5 is 4

so the answer is 10

Shibu  May 23, 2021

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