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# help coordinates

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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-18=x^2+y^2+5x-y?

Jun 27, 2022

### 2+0 Answers

#1
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The area is 47*pi

Jun 27, 2022
#2
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Isolate the constant: $$x^2 + y^2 + 5x - 5y = 18$$

Rearrange as follows: $$(x^2 + 5x) + (y^2 - 5y) = 18$$

Add 6.25 to complete the square on x, and add another 6.25 to complete the square on y.

This gives: $$(x+2.5)^2 + (y-2.5)^2 = 30.5$$.

Note that the constant (30.5) is $$r^2$$, meaning the area of the circle, in terms of pi, is $$\color{brown}\boxed{{30.5 \pi}}$$

Jun 27, 2022