Find the Center and Radius of the Circle $2 x ^ { 2 } + 2 y ^ { 2 } + 8 x + 12 y + 24 = 0$

question 1

Multiple Choice

Find the center and radius of the circle.
- $2 x ^ { 2 } + 2 y ^ { 2 } + 8 x + 12 y + 24 = 0$

• A) \(( - 3 , - 2 ) , \mathrm { r } = 1\)
• B) \(( - 2 , - 3 ) , \mathrm { r } = 1\)
• C) \(( 2,3 ) , r = 1\)
• D) \(( 3,2 ) , \mathrm { r } = 1\)

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Definitions:

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Binomial Expansion

The process of expanding an expression that is raised to a finite power and expressed as a sum of terms using the binomial theorem.

Binomial Coefficient

A number that represents the coefficients in the expansion of a binomial raised to a power, usually expressed as nCk or C(n, k).

Pascal's Triangle

A triangular array of numbers where each number is the sum of the two numbers directly above it, often used in probability theory and algebra.