A circle in the xy -plane has the equation 4x^2+4y^2-24x=28. What is the diameter of the circle?

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Write Circle Equation: Write the given equation of the circle. The given equation is 4x^2 + 4y^2 - 24x = 28. We need to complete the square for both x and y to bring the equation into standard form.Factor Out Coefficients: Factor out the coefficient of x^2 and y^2. Since the coefficients of x^2 and y^2 are both 4, we factor them out to make completing the square easier. 4(x^2 + y^2 - 6x) = 28Complete Square for x: Complete the square for the x-term. To complete the square, we take the coefficient of x, divide it by 2, and square it. Then we add and subtract this value inside the parenthesis. 4(x^2 - 6x + 9 - 9 + y^2) = 28Add Value to Equation: Add the value we subtracted to the other side of the equation. We added and subtracted 9 inside the parenthesis, but since it's multiplied by 4, we need to add 4*9 to the other side of the equation. 4(x^2 - 6x + 9 + y^2) = 28 + 4*9 4(x^2 - 6x + 9 + y^2) = 28 + 36 4(x^2 - 6x + 9 + y^2) = 64Write Completed Square: Write the completed square for the x-term and simplify the equation. (x - 3)^2 is the completed square for the x-term, and we simplify the right side of the equation. 4((x - 3)^2 + y^2) = 64Divide by Coefficient: Divide both sides by the coefficient of the completed squares to get the standard form of the circle's equation. (x - 3)^2 + y^2 = 64 / 4 (x - 3)^2 + y^2 = 16Identify Circle Radius: 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 and r is the radius. From our equation, r^2 = 16, so r = 4.Calculate Circle Diameter: Calculate the diameter of the circle. The diameter (D) of a circle is twice the radius (r), so D = 2r. D = 2 * 4 D = 8

A circle in the $xy$ -plane has the equation $4x^2+4y^2-24x=28$ . What is the diameter of the circle?

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A circle in the xyxyxy-plane has the equation 4x2+4y2−24x=284x^2+4y^2-24x=284x2+4y2−24x=28. What is the diameter of the circle?

A circle in the $xy$ -plane has the equation $4x^2+4y^2-24x=28$ . What is the diameter of the circle?