Find 3 coordinates on the circle when the center of the circle is (4, -3) and the radius is 5
Help me!!! Thank you :)
(x-4)^2 + (y+3)^2 = 25
If x = 4, y = -3 +/- 5
so
(4,-8) or (4,2)
now tell me two more where y = -3
Im still confused about how you got from x=4 to (4, -8)?
First - graph it !!!
If x = 4
(4-4)^2 + (y+3)^2 = 25
0 + (y+3)^2 = 25
y+3 = 5 or -5
y = 2 or y = -8
Sure! To find coordinates on a circle given its center and radius, we can use the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle and r represents the radius.
In this case, we have the center of the circle (4, -3) and the radius of 5. So the equation becomes:
(x - 4)^2 + (y - (-3))^2 = 5^2
Simplifying it further, we get:
(x - 4)^2 + (y + 3)^2 = 25
To find specific coordinates on this circle, we can substitute different values for x and solve for y or vice versa.
Let's choose x = 4 as the first coordinate on the circle. Plugging it into the equation:
(4 - 4)^2 + (y + 3)^2 = 25
0 + (y + 3)^2 = 25
(y + 3)^2 = 25
Taking the square root of both sides, we get:
(y + 3) = ±√25
(y + 3) = ±5
Solving for y, we get two possible coordinates:
1. when y + 3 = 5, y = 2, so the first coordinate is (4, 2).
2. when y + 3 = -5, y = -8, so the second coordinate is (4, -8).
Similarly, we can find more coordinates by substituting different values for x. In this case, let's choose x = 9:
(9 - 4)^2 + (y + 3)^2 = 25
5^2 + (y + 3)^2 = 25
25 + (y + 3)^2 = 25
This equation doesn't have any real solutions, which means there are no coordinates on the circle when x = 9.
So the two coordinates on the circle are (4, 2) and (4, -8).