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

question 18

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 26 feet apart, and the radii of the circles differ by 10 feet. The point $P ( x , y )$ where the circles intersect moves along a curve. Find the equation of the curve.

• A) \[\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 144 } = 1\]
• B) \[\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 288 } = 1\]
• C) \(\quad \frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 144 } = 1\)
• D) \[\frac { ( x - 10 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 144 } = 1\]

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Definitions:

Communication Process Model

A theoretical framework that describes the steps involved in the exchange of information between a sender and a receiver, encompassing elements like encoding, medium, decoding, and feedback.

Potential Areas

Potential areas refer to sectors or fields that hold the possibility for growth, development, or significant contributions in various contexts.

Failure

The state or condition of not meeting a desirable or intended objective, potentially leading to a wide range of consequences.

Non-voice Use

Communication or interaction that occurs without the use of spoken words, such as text or sign language.