Which graph represents the circle given by the equation (x+5)2 + (y+6)2 = 12?
Question
Which graph represents the circle given by the equation (x+5)2 + (y+6)2 = 12?
Solution
The equation of a circle is given by (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.
In the given equation, (x+5)² + (y+6)² = 12, we can see that h = -5, k = -6, and r² = 12. Therefore, the center of the circle is at (-5, -6) and the radius of the circle is √12, which is approximately 3.46.
To graph this, you would:
- Start by drawing a set of axes on a piece of graph paper.
- Mark the point (-5, -6) as the center of the circle.
- Use a compass or a ruler to draw a circle with a radius of √12 (or approximately 3.46 units) around the center point.
The graph that represents this circle would have the center at (-5, -6) and would pass through the points approximately 3.46 units away from the center in all directions.
Similar Questions
To determine the equation of the circle graphed, 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 the origin \((0, 0)\). 2. **Determine the radius of the circle:** The radius is the distance from the center to any point on the circle. From the graph, the circle intersects the x-axis at \(x = 5\) and \(x = -5\), and the y-axis at \(y = 5\) and \(y = -5\). Therefore, the radius \(r\) is 5 units. The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is: \[ (x - h)^2 + (y - k)^2 = r^2\] Since the center is \((0, 0)\) and the radius is 5, the equation of the circle is: \[ (x - 0)^2 + (y - 0)^2 = 5^2\] Simplifying, we get: \[ x^2 + y^2 = 25\] So, the equation of the circle is: \[ x^2 + y^2 = 25\]
Write the equation in standard form for the circle x2=–y2+12y+28.
The equation of a circle is given below. Identify the center and radius. Then graph the circle.=+x2−y224
What is the center of the circle given by the equation (x + 5)2 + (y - 8)2 = 1?
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: \[ \boxed{D} \]
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