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

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

Bytelearn · Accepted Answer

Rewrite equation in standard form: Rewrite the equation of the circle in standard form. The given equation is 4x^2 + 4y^2 - 24x = 28. To rewrite it in standard form, we need to complete the square for the x-terms and move the constant term to the other side. First, factor out the 4 from the x-terms and y-terms: 4(x^2 + y^2 - 6x) = 28 Now, divide both sides by 4 to simplify: x^2 + y^2 - 6x = 7 Next, complete the square for the x-terms by adding (6/2)^2 = 9 to both sides: x^2 - 6x + 9 + y^2 = 7 + 9 Now, the equation becomes: (x - 3)^2 + y^2 = 16Identify the radius: Identify the radius of the circle. 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. Comparing our equation (x - 3)^2 + y^2 = 16 with the standard form, we can see that r^2 = 16. To find the radius r, we take the square root of both sides: r = sqrt(16) r = 4Calculate the diameter: Calculate the diameter of the circle. The diameter of a circle is twice the radius. Diameter = 2 * radius Diameter = 2 * 4 Diameter = 8

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

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

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