Suppose the length of the radius of circle B is 11 units and its center is located 4 units above the origin along the y-axis. Which point is the center of B
Answers
Answer:
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In the standard (x,y) coordinate plane, what is the radius and the center of the circle (x−5)2+(y+4)2=27 ?
Possible Answers:
Center:(−5,4) Radius:33–√
Center:(5,−4) Radius:33–√
Center:(−4,5) Radius:33–√
Center:(−5,4) Radius:27
Center:(5,−4) Radius:27
Correct answer:
Center:(5,−4) Radius:33–√
Explanation:
When finding the center and radius of circle (x−h)2+(y−k)2=r2, the center is (h,k) and the radius is r. Notice that they are not negative even though in the equation they have negative signs in front. This becomes important when dealing with real numbers. Also, notice the square of r.
Our circle, (x−5)2+(y+4)2=27 has the same principles applied as the above principle, therefore (5,−4) is our center. Notice how the numbers signs have been switched. This is the case for all circles due to the negative in the base equation above.
To find the radius of a circle, you must take the number the equation is equal to and square root it. This is due to the square of r mentioned above. The 27−−√=33–√. Use the least common multiples of 27 to find that three 3’s make up 27. Take two threes out as the square root of a number multiplied by itself is itself. This leaves one 3 under the radical. Therefore our radius is 33–√.
Center: (5,−4) Radius: 33