Convert the equation $$x^2 + y^2 - 6x + 8y = 0$$ to standard form.

The standard form is $$(x - 3)^2 + (y + 4)^2 = 25$$ .

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

Substitute the point's coordinates into the circle's equation. If the result is less than r^2, the point is inside; if equal, on the circle; if greater, outside.

What is the equation of a circle with center (7, 0) and radius 3?

The equation is $$(x - 7)^2 + y^2 = 9$$ .

How do you write the equation of a circle given its center and radius?

Use the formula $$(x - h)^2 + (y - k)^2 = r^2$$ , substituting (h, k) for the center and r for the radius.

What is the equation of a circle with center (-4, 2) and radius 6?

The equation is $$(x + 4)^2 + (y - 2)^2 = 36$$ .

What does it mean if the equation of a circle is written as $$x^2 + y^2 = r^2$$ ?

It means the circle is centered at the origin (0, 0) with radius r.

How can you identify the radius from the equation $$x^2 + y^2 = 49$$ ?

The radius is 7, since $$r = \text{sqrt}(49)$$ .

Equations of a Circle 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

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

Back

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

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

Back

The center of the circle is (3, -2).

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the number on the right side of the standard form equation of a circle?

Back

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