+0  
 
0
89
1
avatar

1.A circle has equation (x − 2)2 + (y + 3)2 = 4 and a line has equation 5y − 4x + 20 = 0.

a.What is the distance from the center of the circle to the line?

 

b.What is the greatest distance from a point on the circle to the line?

 May 19, 2020
 #1
avatar+111437 
+1

a)   The  center  of  the circle  is   (2, -3)

 

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

 

l  4(2)  - 5(-3)  - 20  l             l  3 l              3

___________________  = ______  =   ________ 

   sqrt  (4^2 + 5^2)               sqrt 41        sqrt (41)

 

 

b)  greatest  distance  from a point  on the circle to  the  line   =

 

distance found in (a)   +    radius   =

 

3 / sqrt (41)  +  2   

 

 

 

cool cool cool

 May 19, 2020

9 Online Users

avatar
avatar