Stones Dropped into a Calm Pond at Points $A$ And $B$ Create Ripples That Propagate in Widening Circles

question 42

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) \(\quad \frac { ( x - 5 ) ^ { 2 } } { 4 } - \frac { ( y - 4 ) ^ { 2 } } { 32 } = 1\)
• 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:

Job-Order Costing

A cost accounting system that accumulates manufacturing costs separately for each job or order, suitable for industries producing customized products.

Overapplied Overhead

A situation where the allocated overhead cost in accounting is more than the actual overhead incurred.

Underapplied Overhead

The amount by which the actual manufacturing overhead cost exceeds the applied overhead cost.

Job-Order Costing

Job-order costing is a costing method used to determine the cost of manufacturing each custom-made product or job, particularly effective for individual or special products.