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

The general form is $$x^2 + y^2 + Dx + Ey + F = 0$$ , where D, E, and F are constants.

If the equation of a circle is $$(x+1)^2 + (y-5)^2 = 25$$ , what is the center and radius?

The center is (-1, 5) and the radius is 5 units.

What does the term 'radius' mean 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 graph the equation of a circle?

To graph, identify the center (h, k) and radius r, then plot the center and draw a circle with radius r around it.

What is the significance of the value on the right side of the equation in standard form?

The value on the right side of the equation $$(x-h)^2 + (y-k)^2 = r^2$$ represents the square of the radius.

What is the equation of a circle with center (0, 0) and radius 4?

The equation is $$x^2 + y^2 = 16$$ .

How do you determine if a point lies inside, on, or outside a circle?

Substitute the point (x, y) into the circle's equation. If the result is less than r^2, it's inside; equal to r^2, it's on; greater than r^2, it's outside.

What is the relationship between the diameter and radius of a circle?

The diameter is twice the radius, so $$d = 2r$$ .

Equations of Circles Flashcards

Student preview

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 radius from the equation of a circle?

Back

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

Convert the equation x² + y² + 4x + 6y - 36 = 0 to standard form.

Back

5.

FLASHCARD QUESTION

Front

Back

The radius is 4 units, since r^2 = 16.

6.

FLASHCARD QUESTION

Front

What is the equation of a circle with center (4, -2) and radius 3?

Back

7.

FLASHCARD QUESTION

Front

How do you complete the square for the equation of a circle?

Back

To complete the square, rearrange the equation to group x and y terms, then add the necessary constants to both sides to form perfect squares.

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