How do you determine the radius from the standard form of a circle?

The radius can be determined by taking the square root of the constant on the right side of the standard form equation.

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

In the general form $$x^2 + y^2 + Dx + Ey + F = 0$$ , the center can be found using the formulas $$(-\frac{D}{2}, -\frac{E}{2})$$ .

How do you convert the equation $$x^2 + 4x + y^2 - 6y - 12 = 0$$ to standard form?

Complete the square for x and y: $$(x+2)^2 + (y-3)^2 = 25$$ .

What is the formula for the distance from the center to a point on the circle?

The distance from the center (h, k) to a point (x, y) on the circle is given by the radius r, where $$r = \text{distance} = \text{sqrt}((x-h)^2 + (y-k)^2)$$ .

What does the term 'radius' refer to in the context of a circle?

The radius is the distance from the center of the circle to any point on its circumference.

How can you identify the center and radius from the equation $$x^2 + y^2 + 14x - 2y = -14$$ ?

Rearranging gives the center (-7, 1) and radius 6 units after completing the square.

What is the effect of changing the sign of the radius in the equation of a circle?

The radius must always be a positive value; a negative radius does not have a geometric meaning.

What is the importance of the constant term in the equation of a circle?

The constant term affects the size of the circle; it determines the radius when the equation is in standard form.

LT-4a CYU Equation of Circle (Complete the Square) (fall) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

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

Back

2.

FLASHCARD QUESTION

Front

How do you find the center of a circle from its equation?

Back

3.

FLASHCARD QUESTION

Front

What is the radius of a circle in standard form?

Back

4.

FLASHCARD QUESTION

Front

How do you rewrite the equation of a circle in standard form?

Back

To rewrite the equation of a circle in standard form, group the x and y terms, complete the square for each, and rearrange the equation.

5.

FLASHCARD QUESTION

Front

What does completing the square involve?

Back

6.

FLASHCARD QUESTION

Front

Back

The center is (-3, 6) and the radius is 4 units.

7.

FLASHCARD QUESTION

Front

What is the significance of the center in a circle?

Back

The center of a circle is the point from which all points on the circle are equidistant.

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