The ratio of the area of circle C to circle E is 16/9.
Hence, option B is the right choice.
How is the area of a circle determined?
The area of a circle is the product of π, a constant, and the square of its radius (r). The radius of the circle is any line connecting the center of the circle to any point on its circumference (boundary).
Therefore, the area of a circle = πr².
How to solve the question?
In the question, we are asked to determine the ratio of the area of circle C to circle E, from the given diagram.
In the diagram, for circle C,
The center is at the point (-3, 1).
For radius, we choose the point (1, 1) on the circumference.
Therefore, radius = √((1 - (-3))² + (1 - 1)²) {using the distance formula between the point (x1, y1) and (x2, y2), given as:
d = √((x1 - x2)² + (y1 - y2)²)}.
or, radius = √(4)² = √16 = 4.
Therefore, area = πr² = π4² = 16π.
In the diagram, for circle E,
The center is at the point (4, 9).
For radius, we choose the point (1, 9) on the circumference.
Therefore, radius = √((1 - 4)² + (1 - 1)²) {using the distance formula between the point (x1, y1) and (x2, y2), given as:
d = √((x1 - x2)² + (y1 - y2)²)}.
or, radius = √(-3)² = √9 = 3.
Therefore, area = πr² = π3² = 9π.
Therefore, the ratio of the area of circle C to circle E = 16π/9π = 16/9.
Hence, option B is the right choice.
Learn more about the area of a circle at
https://brainly.com/question/22685822
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