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What is the area enclosed by the region defined by the equation x^2+y^2+10x+24y=0?

 Nov 15, 2019
 #1
avatar+2557 
+1

Hint: Find the radius

 

Do that by putting it into standard form.

 Nov 15, 2019
 #2
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0

i dont know how to do the see...

 Nov 15, 2019
 #3
avatar+2557 
+2

do the see?

CalculatorUser  Nov 15, 2019
 #4
avatar+679 
+1

HAHA nice joke CU, 
But guest....
what do you not understand about these? do you have a specific question that we can help you with that does not include any math problems? 

Nirvana  Nov 15, 2019
 #5
avatar+2557 
+1

Yeah I was trying to get the guest to reply because I was confused by "do the see"

CalculatorUser  Nov 15, 2019
 #6
avatar+8848 
+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 15, 2019

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