A circle in the xy-plane has the equation 2x^(2)+2y^(2)-8x-5y-(55)/(8)=0". " What is the diameter of the circle?

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A circle in the  xy-plane has the equation  2x^(2)+2y^(2)-8x-5y-(55)/(8)=0". " What is the diameter of the circle?

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Rewrite Equation: Rewrite the given equation of the circle in a more standard form by completing the squares for x and y. 2x^2 + 2y^2 - 8x - 5y - (55/8) = 0 Divide the entire equation by 2 to simplify the coefficients of x^2 and y^2. x^2 + y^2 - 4x - (5/2)y - (55/16) = 0Complete Squares: Complete the square for the x-terms. Add (4/2)^2 = 4 to both sides of the equation to complete the square for x. x^2 - 4x + 4 + y^2 - (5/2)y - (55/16) = 4Combine Terms: Complete the square for the y-terms. Add ((5/2)/2)^2 = (25/16) to both sides of the equation to complete the square for y. x^2 - 4x + 4 + y^2 - (5/2)y + (25/16) - (55/16) = 4 + (25/16)Identify Radius: Combine like terms and rewrite the equation in standard form. (x - 2)^2 + (y - (5/4))^2 = 4 + (25/16) + (55/16) (x - 2)^2 + (y - (5/4))^2 = 4 + (80/16) (x - 2)^2 + (y - (5/4))^2 = 4 + 5 (x - 2)^2 + (y - (5/4))^2 = 9Calculate Diameter: Identify the radius of the circle from the standard form equation. The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. From the equation (x - 2)^2 + (y - (5/4))^2 = 9, we can see that the radius r is the square root of 9, which is 3.Calculate the diameter of the circle using the radius. The diameter D of a circle is twice the radius, so D = 2r. D = 2 * 3 = 6

A circle in the $x y$ -plane has the equation $\newline$ $2 x^{2}+2 y^{2}-8 x-5 y-\frac{55}{8}=0 \text {. }$ $\newline$ What is the diameter of the circle?

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A circle in the xy x y xy-plane has the equation\newline2x2+2y2−8x−5y−558=0. 2 x^{2}+2 y^{2}-8 x-5 y-\frac{55}{8}=0 \text {. } 2x2+2y2−8x−5y−855​=0. \newlineWhat is the diameter of the circle?

A circle in the $x y$ -plane has the equation $\newline$ $2 x^{2}+2 y^{2}-8 x-5 y-\frac{55}{8}=0 \text {. }$ $\newline$ What is the diameter of the circle?