The center of a circle is located at (–5, 2) and a point on the circle is located at (5, -22). Which other points are also on the circle?
(-29, -8)
(-31, 5)
(5, 26)
(19, 12)
(19, -6)
So the answers i got that work is
1.(-31,5)
2.(-29,-8)
3.(19,12)
That is what i got and i keep getting it wrong
(x + 5)^2 + (y - 2)^2 = 676
plug in the points to check if they lie on the circle
got it
To determine which points are on the given circle with the center at (-5, 2) and a point on the circle at (5, -22), we can use the distance formula. The distance between the center of the circle and any point on the circle should be equal to the radius.
1. Calculate the distance between the center and the given point:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(5 - (-5))^2 + (-22 - 2)^2]
= √[10^2 + (-24)^2]
= √[100 + 576]
= √676
= 26
2. Now, calculate the distance between the center and each of the other given points:
a. (-29, -8):
Distance = √[(-29 - (-5))^2 + (-8 - 2)^2]
= √[(-24)^2 + (-10)^2]
= √[576 + 100]
= √676
= 26
b. (-31, 5):
Distance = √[(-31 - (-5))^2 + (5 - 2)^2]
= √[(-26)^2 + 3^2]
= √[676 + 9]
= √685
≈ 26.18
c. (5, 26):
Distance = √[(5 - (-5))^2 + (26 - 2)^2]
= √[10^2 + 24^2]
= √[100 + 576]
= √676
= 26
d. (19, 12):
Distance = √[(19 - (-5))^2 + (12 - 2)^2]
= √[24^2 + 10^2]
= √[576 + 100]
= √676
= 26
e. (19, -6):
Distance = √[(19 - (-5))^2 + (-6 - 2)^2]
= √[24^2 + (-8)^2]
= √[576 + 64]
= √640
≈ 25.3
From the calculations, we can see that the points (-29, -8), (5, 26), and (19, 12) are not on the circle because their distances from the center are not equal to the radius (26). Only the point (-31, 5) lies on the circle.