Is the equation correct?
A circle has a diameter of 12 with a center translated 18 units left and 7 units down from the origin.
1. Write an equation for the circle.
(x + 18) ^2 + (y + 7)^2
( x + 18 )² + ( y + 7 )² = 12²
( x + 18 )² + ( y + 7 )² = 144
I am sure Bosnian meant:
( x + 18 )² + ( y + 7 )² = 6² , since the radius is 6, not 12
( x + 18 )² + ( y + 7 )² = 36
To determine if the equation given is correct, we need to compare it with the general equation of a circle. The general equation of a circle with a center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
In this case, we are given that the center is translated 18 units left and 7 units down from the origin. Therefore, the center of the circle is (-18, -7).
Comparing this with the given equation:
(x + 18)^2 + (y + 7)^2
We can observe that the signs have been reversed from the general equation, but this is not an issue as the distance squared is what matters. Therefore, the equation given is correct and represents a circle with a diameter of 12 units and a center translated 18 units left and 7 units down from the origin.