147k views
1 vote
Determina el centro y el radio de las circunferencias representadas por las ecuaciones:

a) (x + 1)² + (y - 3)² = 5
b) 5x² - y² +6=0
c) x² + y² - 4x - 10y + 20 = 0

1 Answer

4 votes

To determine the center and radius of the given circles, compare the equations with the standard equation. For question a, the center is (-1, 3) and the radius is sqrt(5). For question b, the center is (0, 0) and the radius is sqrt(1/6). For question c, the center is (2, 5) and the radius is 3.

Question a:

To determine the center and radius of the circle represented by the equation (x + 1)² + (y - 3)² = 5, we can compare it with the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. By comparing the equations, we can see that the center of the circle is (-1, 3) and the radius is sqrt(5).

Question b:

To express the equation 5x² - y² +6=0 in a coordinate system with the origin at the center, we can divide the equation by 6 to obtain (5/6)x² - (1/6)y² + 1 = 0. Comparing this with the standard equation of a circle, we can determine that the center is at the origin (0, 0) and the radius is sqrt(1/6).

Question c:

To determine the center and radius of the circle represented by the equation x² + y² - 4x - 10y + 20 = 0, we can complete the square by rearranging the equation to (x² - 4x) + (y² - 10y) = -20. Completing the square for x and y, we get (x - 2)² + (y - 5)² = 9. Comparing this with the standard equation of a circle, we can determine that the center is (2, 5) and the radius is 3.

User Xaphod
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories