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find the standard equation of the circle of radius 2 that are tangent to both the line x=1 and y=3 .

 Nov 18, 2019
 #1
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+1

The radius is 2   so we know the center will be   2   from x = 1      h = 3

                        and the center will be 2 away frm y = 3                 k=1

h,k = 3,1   r^2 = 4

 

(x-3)^2 + (y-1)^2 = 4 

 Nov 18, 2019
 #2
avatar+105370 
+2

Actually....we have four possibilities......

 

The center  of the first circle  is   (3, 1)

Its equation is (x - 3)^2 + (y - 1)^2  =4

 

Another possibility is a circle with a center of ( 3, 5)

Its equation is  ( x - 3)^2 + ( y - 5)^2  = 4

 

Two other possibilites  

A circle with a center of (-1, 1)

Equation is  ( x + 1)^2 + ( y - 1)^2  = 4

A circle with a center (-1,5)

Equation is ( x + 1)^2 + ( y - 5)^2  = 4

 

See the graph here : https://www.desmos.com/calculator/lgpofoe62f

 

 

cool cool cool

 Nov 18, 2019
 #3
avatar+19726 
+1

Nice !  I forgot about the other THREE !

ElectricPavlov  Nov 18, 2019
 #4
avatar+60 
+1

thank you 

shgg111  Nov 18, 2019

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