Question

1 What are the center and the radius of the circle

冯宇婷 6362
3 6362
whose equation is (x - 5)² + (y + 3)² = 16?
1) (-5,3) and 16
2)
3)
4)
500 6362
6362
(5,-3) and 16
(-5,3) and 4
(5,-3) and 4
15 6362
75 6362
冯宇婷 6362
5 6362
冯宝婷 6362

Answer 1

The center of the circle is (5, -3) and the radius is 4, based on the standard form of the equation for a circle.

Step-by-step explanation:

The equation given is in the standard form for a circle, (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. The equation provided is (x - 5)² + (y + 3)² = 16. Here, the center (h, k) is thus (5, -3) comparing with the standard form. As for the radius, the equation is equal to r², so taking the square root of 16 gives us r = 4. Therefore, the correct answer is the center is (5, -3) and the radius is 4.

The equation (x - 5)² + (y + 3)² = 16 represents a circle. To find the center and radius of the circle, we can compare the given equation to the standard equation of a circle, which is (x - h)² + (y - k)² = r². In this case, the center of the circle is (5, -3) and the radius is 4. The center coordinates are obtained by taking the opposite sign of the numbers inside the parentheses, while the radius is the square root of the number after the equal sign.