Circle Equation Flashcard-MK

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Front

How do you convert a circle's equation from general form to standard form?

Back

To convert from general form (Ax² + Ay² + Bx + Cy + D = 0) to standard form, complete the square for the x and y terms.

Front

What is the result of expanding (x + a)²?

Back

The result of expanding (x + a)² is x² + 2ax + a².

Front

What is the result of expanding (y - b)²?

Back

The result of expanding (y - b)² is y² - 2by + b².

Front

What is the binomial theorem?

Back

The binomial theorem describes the algebraic expansion of powers of a binomial, expressed as (a + b)ⁿ = Σ (n choose k) a^(n-k) b^k.

Front

What does completing the square involve?

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² = q, making it easier to analyze and solve.

Front

What is the significance of the center and radius in a circle's equation?

Back

The center (h, k) indicates the circle's location on the coordinate plane, while the radius r determines its size.

Front

How do you identify the center and radius from the standard form of a circle's equation?

Back

From the standard form (x - h)² + (y - k)² = r², the center is (h, k) and the radius is r.

Front

What is the formula for the distance between two points (x₁, y₁) and (x₂, y₂)?

Back

The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

What is the relationship between the coefficients in the general form of a circle's equation?

Back

In the general form x² + y² + Dx + Ey + F = 0, the coefficients D, E, and F relate to the circle's center and radius.