Stones Dropped into a Calm Pond at Points a and B

question 73

Multiple Choice

Stones dropped into a calm pond at points A and B create ripples that propagate in widening circles.In the figure below, points A and B are 12 feet apart, and the radii of the circles differ by 4 feet.The point
P (x, y) where the circles intersect moves along a curve.Find the equation of the curve.

• A) \(\quad \frac { ( x - 4 ) ^ { 2 } } { 4 } - \frac { ( y - 4 ) ^ { 2 } } { 32 } = 1\)
• B) \(\quad \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 32 } = 1\)
• C) \(\quad \frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 64 } = 1\)
• D) \(\quad \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 32 } = 1\)
• E) none of these

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Definitions:

Right-Skewed

A description of a distribution of data where the tail on the right side of the histogram is longer or fatter than the left side, indicating that the mean is greater than the median.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values in the data set deviate from the mean.

Mean

A measure of central tendency that is calculated by dividing the sum of all values in a dataset by the number of values.

Right-Skewed

Refers to a distribution where the tail on the right side of the histogram is longer or fatter than the left side.