hectictar

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Usernamehectictar
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Questions 9
Answers 2820

 #6
avatar+8891 
+1

This is the equation of a circle. See: https://www.desmos.com/calculator/z1xxnd2tgl

 

To get it into "standard form" as CU was saying, we need to complete both squares.

 

x2 + y2 + 10x + 24y  =  0

                                                    Rearrange the terms.

x2 + 10x + y2 + 24y  =  0

                                                    Add  (10/2)2  which is  25  to both sides to complete the first square.

x2 + 10x + 25  +  y2 + 24y  =  25

                                                                Add  (24/2)2  which is  144  to both sides to complete the second square.

x2 + 10x + 25  +  y2 + 24y + 144  =  169

                                                                Factor both perfect square trinomials.

(x + 5)2  +  (y + 12)2  =  169

 

Now the equation is in the form we want. So we can see

 

r2  =  169     , where  r  is the radius of the circle. And so

 

area of the circle   =   π r2   =   169π

Nov 14, 2019
 #1
avatar+8891 
+1
Nov 14, 2019
 #6
avatar+8891 
+2
Nov 14, 2019