The equation of a circle is given below. Identify the center and radius. Then graph the circle. \( (x-2)^{2}+(y-5)^{2}=16 \)
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The center of the circle is the point \( (2, 5) \). The radius can be found by taking the square root of the right side of the equation \( \sqrt{16} \), which gives us a radius of 4. To graph the circle, plot the center at \( (2, 5) \) and then from that point, measure out 4 units in all directions (up, down, left, right) to mark the circle's edge. Finally, connect these points in a smooth, rounded shape to complete the circle! To really understand circles, you might want to explore the properties of conic sections. They pop up in everything from planetary orbits to architectural designs. The elegant curves of circles can lead you to fascinating discoveries in both mathematics and nature, like the ripple effects on water when a stone drops into it!
