Questions: Give the center and radius, then sketch the graph of the circle: (x-2)^2+(y+4)^2=4

Give the center and radius, then sketch the graph of the circle: (x-2)^2+(y+4)^2=4
Transcript text: Give the center and radius, then sketch the graph of the circle: $(x-2)^{2}+(y+4)^{2}=4$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the center and radius of the circle

The given equation of the circle is \((x - 2)^2 + (y + 4)^2 = 4\). This is in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

  • Center \((h, k)\): \((2, -4)\)
  • Radius \(r\): \(\sqrt{4} = 2\)
Step 2: Plot the center of the circle

On the given graph, locate the point \((2, -4)\) and mark it as the center of the circle.

Step 3: Draw the circle with the given radius

From the center \((2, -4)\), measure a distance of 2 units in all directions (up, down, left, right) and draw the circle passing through these points.

Final Answer

  • Center: \((2, -4)\)
  • Radius: \(2\)
  • Graph: Circle centered at \((2, -4)\) with radius 2 units.
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following is a valid reason why the quadrilateral shown below is a parallelogram? A. Both pairs of opposite angles are congruent. B. Both pairs of opposite sides are parallel. C. Both pairs of consecutive angles are complementary. D. Both pairs of consecutive angles are supplementary.
failedAnswered
After the creation and implementation of a vaccine, the number of people that catch a disease falls by 40% every 12 days. Given this, compute the per-day rate of decay of the number of people that catch the disease. Give as a percentage, without the percent symbol, accurate to two decimal places (for example, if your answer is 12.6821%, you should input 12.68).
failedAnswered
V=(h^3-3)(2h^2-2h-3)
failedAnswered
A. lateral pterygoid process B. perpendicular plate C. styloid process D. lesser wing E. manubrium
failedAnswered
There are three libraries in Glen city. Each library has fiction and non-fiction books available. The double bar graph below shows how many of each. Interpreting a double bar graph library. Use this graph to answer the questions. (a) Which libraries have more fiction books than non-fiction books? Check all that apply. - Central - Woodside - Coast (b) Which libraries have fewer than 600 fiction books? Check all that apply.