Circle 1: center \( (2,3) \) and radius 4

Did you know that the equation of a circle is a classic gem in geometry? For Circle 1, with its center at \( (2,3) \) and a radius of 4, the equation can be written as \( (x - 2)^2 + (y - 3)^2 = 16 \). The 16 comes from squaring the radius (4), giving you a complete picture of all the points that make up this circle! Now, let’s consider a fun application of circles. Take that circle and imagine it on a coordinate plane! You could plot it to determine how it intersects with lines or other shapes. This is super useful in fields like engineering and computer graphics, where understanding the relationship between different geometric figures can lead to innovative designs or solutions to complex problems. So, grab your graph paper and start drawing!