\( \equiv 1 \quad \equiv 2 \) 3 4 5 6 7 Is the point \( (-12,-14) \) on the circle defined by \( (x+12)^{2}+(y+17)^{2}=9 \) ? Yes No

To determine whether the point \((-12, -14)\) lies on the circle defined by the equation \((x + 12)^2 + (y + 17)^2 = 9\), we can substitute the coordinates of the point into the equation and see if it holds true. 1. **Substitute \(x = -12\) and \(y = -14\) into the equation:** \[ (x + 12)^2 + (y + 17)^2 = (-12 + 12)^2 + (-14 + 17)^2 \] 2. **Simplify the expressions inside the parentheses:** \[ (0)^2 + (3)^2 = 0 + 9 = 9 \] 3. **Compare the result with the right side of the equation:** \[ 9 = 9 \] Since both sides of the equation are equal, the point \((-12, -14)\) satisfies the equation of the circle. **Answer:** Yes