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In terms of pi, what is the area of the circle defined by the equation 2x^2+2y^2+10x-6y-48=0

 
 Aug 2, 2022

Best Answer 

 #1
avatar+2275 
+2

Simplify: \(x^2 + y^2 + 5x - 3y - 24 = 0 \)

 

Add \(1.5^2 \) and \(2.5^2\) to both sides to complete the square: \(x^2 + y^2 + 5x - 3y - 24 + 1.5^2 + 2.5^2 = 1.5^2 + 2.5^2\)

 

Now, add 24 to both sides: \(x^2 + y^2 + 5x - 3y + 1.5^2 + 2.5^2 = 24 + 1.5^2 + 2.5^2\)

 

Complete the square on x: \((x+2.5)^2 + y^2 - 3y - 24 = 1.5^2 + 2.5^2\)

 

Complete the square on y: \((x+2.5)^2 + (y-1.5)^2 = 1.5^2 +2.5^2 + 24\)

 

Simplify the right-hand side: \((x+2.5)^2 + (y - 1.5)^2 = 32.5\)

 

The radius of this circle is \(\sqrt{32.5}\), so the area is \(\color{brown}\boxed{32.5 \pi}\)

 
 Aug 2, 2022
 #1
avatar+2275 
+2
Best Answer

Simplify: \(x^2 + y^2 + 5x - 3y - 24 = 0 \)

 

Add \(1.5^2 \) and \(2.5^2\) to both sides to complete the square: \(x^2 + y^2 + 5x - 3y - 24 + 1.5^2 + 2.5^2 = 1.5^2 + 2.5^2\)

 

Now, add 24 to both sides: \(x^2 + y^2 + 5x - 3y + 1.5^2 + 2.5^2 = 24 + 1.5^2 + 2.5^2\)

 

Complete the square on x: \((x+2.5)^2 + y^2 - 3y - 24 = 1.5^2 + 2.5^2\)

 

Complete the square on y: \((x+2.5)^2 + (y-1.5)^2 = 1.5^2 +2.5^2 + 24\)

 

Simplify the right-hand side: \((x+2.5)^2 + (y - 1.5)^2 = 32.5\)

 

The radius of this circle is \(\sqrt{32.5}\), so the area is \(\color{brown}\boxed{32.5 \pi}\)

 
BuilderBoi Aug 2, 2022

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