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# 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=0?

Jun 28, 2022

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Isolate the constant: $$2x^2 + 2y^2 + 10x - 6y = 18$$

Divide the entire equation by 2: $$x^2 + y^2 + 5x - 3y = 9$$

Add $$8.5$$ to both sides so we can complete the square for both x and y: $$x^2 + y^2 + 5x - 3y +8.5= 17.5$$

Complete the square: $$(x+2.5)^2 + (y - 1.5)^2 = 17.5$$

Note the constant on the left-hand side equals the radius of the circle squared, meaning the area of the circle is $$\color{brown}\boxed{17.5 \pi}$$

Jun 28, 2022