Find the Equation of the Circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$

question 296

Multiple Choice

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. $( 0,0 ) , ( 0,12 ) , ( 6,6 )$

• A) \(x ^ { 2 } - y ^ { 2 } + 12 y = 0\)
• B) \(x ^ { 2 } - y ^ { 2 } - 12 y = 0\)
• C) \(- x ^ { 2 } + y ^ { 2 } - 12 y = 0\)
• D) \(x ^ { 2 } + y ^ { 2 } - 12 y = 0\)
• E) \(x ^ { 2 } + y ^ { 2 } + 12 y = 0\)

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Definitions:

Synergistic Interaction

A phenomenon where combined actions of different elements produce an effect greater than the sum of their separate effects.

Exponential Growth

Rapid increase in a quantity where the rate of growth is proportional to the current size, leading to ever-larger increases over time.

Carrying Capacity

The maximum population size that an environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment.

Molecules

The smallest unit of a chemical compound that can exist, consisting of two or more atoms bonded together.