Expand the expression $$(x - a)^2$$ .

The expansion is $$x^2 - 2ax + a^2$$ .

Expand the expression $$(y - b)^2$$ .

The expansion is $$y^2 - 2by + b^2$$ .

What is the significance of the radius in the context of a circle?

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

How do you convert the equation of a circle from general form to standard form?

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for x and y.

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

In the general form, the coefficients of $$x^2$$ and $$y^2$$ must be equal for the equation to represent a circle.

What is the binomial expansion of $$(x - 5)^2$$ ?

The binomial expansion is $$x^2 - 10x + 25$$ .

How do you find the vertex of a parabola given its equation in standard form?

The vertex can be found using the formula $$(h, k)$$ from the equation $$y = a(x - h)^2 + k$$ .

What is the difference between the general form and the standard form of a circle's equation?

The general form is $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ , while the standard form is $$(x - h)^2 + (y - k)^2 = r^2$$ .

What does the term 'completing the square' mean in algebra?

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial.

Circle Equation Flashcard Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

2.

FLASHCARD QUESTION

Front

How do you convert a quadratic expression into binomial form?

Back

To convert a quadratic expression into binomial form, complete the square or factor the expression.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the formula for the radius of a circle given its equation in standard form?

Back

5.

FLASHCARD QUESTION

Front

What does the center of a circle represent in its equation?

Back

The center (h, k) represents the point in the Cartesian plane around which the circle is drawn.

6.

FLASHCARD QUESTION

Front

How do you identify the center and radius from the equation of a circle?

Back

7.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

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