What are the equations of the circles tangent to the x-axis, of radius 4 and whose center is at (-2,y)
Please help, how do I solve this problem?
Since (-2,0) must be on the circle , (it is tangent to that point)
y must be either 4 or -4
first case: y = 4
centre is (-2,4) radius is 4
equation: (x+2)^2 + (y-4)^2 = 16
you try the other circle with centre (-2,-4)
-2,-4
To find the equation of a circle, we need to know the coordinates of its center and its radius. In this case, we know that the center is at (-2, y) and the radius is 4.
The equation of a circle can be written as (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center, and r represents the radius.
Since the circle is tangent to the x-axis, it means that the distance between the center and the x-axis is equal to the radius.
Therefore, we have the following equation: y - k = r
Substituting the given values into the equation, we get:
y - y-coordinate of the center = radius
y - (-2) = 4
y + 2 = 4
y = 4 - 2
y = 2
So, the y-coordinate of the center is 2.
Now we can write the equation of the circle:
(x - (-2))^2 + (y - 2)^2 = 4^2
(x + 2)^2 + (y - 2)^2 = 16
Therefore, the equation of the circle with center (-2, 2) and radius 4, which is tangent to the x-axis, is (x + 2)^2 + (y - 2)^2 = 16.
To solve this problem, we can use the equation of a circle.
The general equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) are the coordinates of the center of the circle and r is the radius.
In this case, the center of the circle is (-2, y), and the radius is 4. Since the circle is tangent to the x-axis, it means that the y-coordinate of the center will be equal to the radius.
So, we have (x - (-2))^2 + (y - y)^2 = 4^2.
The equation simplifies to (x + 2)^2 + y^2 = 16.
Hence, the equation of the circles tangent to the x-axis, with a radius of 4 and a center at (-2, y), is (x + 2)^2 + y^2 = 16.