Question

Circle O has a center at (-2, -2) and a diameter of 10 units. Which point lies on Circle O?

Answer 1

The point (1, 2) lies on Circle O

Step-by-step explanation:

The center of circle O is given as (-2, -2) and the diameter is 10 units. We know that the coordinates of the center point (h, k) represent the center of the circle. So, in this case, the center is at (-2, -2). Additionally, the diameter of a circle is twice the length of its radius, so the radius of circle O is 5 units.

Now, we can find the equation of the circle in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Substituting the given values, the equation of circle O is (x + 2)^2 + (y + 2)^2 = 5^2.

To find which point lies on Circle O, we can substitute the coordinates of the point into the equation of the circle. If the point satisfies the equation, then it lies on the circle.

Let's take an example point (1, 2). Substituting these values into the equation, we get (1 + 2)^2 + (2 + 2)^2 = 5^2. Simplifying, we have 9 + 16 = 25, which is true. Therefore, the point (1, 2) lies on Circle O.

Answer 2

hello :
an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =-2 and b = 2 (Center at the point A(-2;-2))
r= 10/2=5
the equation is : (x+2)² +(y+2)² =25