1. **State the problem:** We have a circle defined by the equation $$x^2 + y^2 = 25$$ and the slope of the tangent line at any point on the circle is given by $$\frac{dy}{dx} = -\frac{x}{y}$$. We are also given a velocity value at a specific time, but since acceleration $$a(t) = 0$$, the velocity is constant. 2. **Understand the circle equation:** The equation $$x^2 + y^2 = 25$$ represents a circle centered at the origin with radius $$5$$ because $$\sqrt{25} = 5$$. 3. **Find the slope of the tangent line:** The derivative $$\frac{dy}{dx} = -\frac{x}{y}$$ tells us the slope of the tangent line at any point $$(x,y)$$ on the circle. 4. **Interpret velocity and acceleration:** Given $$a(t) = 0$$, acceleration is zero, meaning velocity is constant. The velocity at time $$t=16.2$$ is $$4.025$$, so velocity $$v(t) = 4.025$$ for all $$t$$. 5. **Summary:** The circle's geometry and slope formula describe the tangent lines, and the velocity is constant due to zero acceleration. **Final answer:** The circle is $$x^2 + y^2 = 25$$ with tangent slope $$\frac{dy}{dx} = -\frac{x}{y}$$ and constant velocity $$v(t) = 4.025$$.