The solution set of an equation of a circle is all of the points that lie in the circle.

The solution set of an equation of a circle is all of the points that lie on the circle.A.TrueB.FalseSUBMITarrow_backPREVIOUS

The equation of a circle is 4x2 + 4y 2− 24x − 32y - 96 = 0.  Write the equation in standard form.Question 7Select one:a.(x - 3)2 + (y - 4)2 = 49b.(x - 3)2 + (y + 4)2 = 49c.(x + 3)2 + (y - 4)2 = 49d.(x - 3)2 + (y - 4)2 = -49

Which of the following is the equation for a circle with a radius of r and center at (h, v)?A.h2 + v2 = r2B.(x - v)2 + (y - h)2 = r2C.(x + h)2 + (y + v)2 = r2D.(x - h)2 + (y - v)2 = r2SUBMITarrow_backPREVIOUS

The circle below is centered at the point (4, -3) and has a radius of length 3. What is its equation?A.(x - 3)2 + (y + 4)2 = 9B.(x - 3)2 + (y - 4)2 = 9C.(x - 4)2 + (y + 3)2 = 32D.(x + 4)2 + (y - 3)2 = 32SUBMITarrow_backPREVIOUS

To determine which equation represents the circle shown in the figure, we need to identify the center and the radius of the circle. 1. **Identify the center of the circle:** From the graph, the center of the circle is at \((-1, 1)\). 2. **Identify the radius of the circle:** The radius can be determined by measuring the distance from the center to any point on the circle. From the graph, the radius is 2 units. 3. **Write the standard form of the equation of a circle:** The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is: \[ (x - h)^2 + (y - k)^2 = r^2 \] 4. **Substitute the center and radius into the equation:** The center is \((-1, 1)\) and the radius is 2. Therefore: \[ (x - (-1))^2 + (y - 1)^2 = 2^2 \] Simplifying, we get: \[ (x + 1)^2 + (y - 1)^2 = 4 \] 5. **Match with the given options:** The correct equation is: \[ (x + 1)^2 + (y - 1)^2 = 4 \] Therefore, the correct answer is: \[ \boxed{D} \]