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Compute the area enclosed by the ellipse ((x)/(c))² + ((y)/(d))² = 1, where c and d are positive constants. What is the area of the enclosed region?

User DOSMarter
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Final answer:

The area of the ellipse described by the equation ((x)/(c))^2 + ((y)/(d))^2 = 1 is πcd, where c and d are the semi-major and semi-minor axes of the ellipse, respectively.

Step-by-step explanation:

The area enclosed by the ellipse ((x)/(c))^2 + ((y)/(d))^2 = 1, where c and d are positive constants, is given by the formula A = πcd. Here, c represents half the length of the major axis (the longest diameter of the ellipse) and d represents half the length of the minor axis (the shortest diameter of the ellipse). The symbol π (pi) represents the mathematical constant approximately equal to 3.14159, which is the ratio of the circumference of a circle to its diameter. To compute the area of the given ellipse, we simply multiply the values of c and d together and then multiply this product by π. This yields the area A of the ellipse, which is the region enclosed within its boundary.

User JeanMertz
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