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

The general form is $$x^2 + y^2 + Dx + Ey + F = 0$$ .

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

To convert, complete the square for the x and y terms.

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

The radius determines the size of the circle; larger radius means a larger circle.

What is the relationship between the center and radius in a circle?

The center is a fixed point from which all points on the circle are equidistant, with that distance being the radius.

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

The equation is $$(x-h)^2 + (y-k)^2 = r^2$$ .

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

Substitute the point 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 does it mean if the radius is zero in the equation of a circle?

If the radius is zero, the circle is reduced to a single point, which is the center.

How can you find the diameter of a circle from the radius?

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

Equation of Circle 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

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

Back

3.

FLASHCARD QUESTION

Front

How do you find the radius from the equation of a circle?

Back

4.

FLASHCARD QUESTION

Front

Back

The center of the circle is (0, 0).

5.

FLASHCARD QUESTION

Front

Write the equation of a circle with center at (2, 3) and radius 5.

Back

6.

FLASHCARD QUESTION

Front

Back

Center: (2, -5), Radius: 9.

7.

FLASHCARD QUESTION

Front

Write the equation of a circle with center C(-5, 8) and radius = 7.

Back

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