What is the radius of a circle if its equation is $$(x - 4)^2 + (y - 3)^2 = 25$$ ?

The radius is $$r = \text{sqrt}(25) = 5$$ units.

If a circle has a center at (2, -3) and a radius of 6, what is its equation?

The equation is $$(x - 2)^2 + (y + 3)^2 = 36$$ .

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

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

What is the significance of the value on the right side of the circle's equation?

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

Find the center of a circle given the endpoints of a diameter at (4, 6) and (10, 2).

The center is $$igg( \frac{4 + 10}{2}, \frac{6 + 2}{2} igg) = (7, 4)$$ .

What is the equation of a circle with center (-1, 2) and radius 5?

The equation is $$(x + 1)^2 + (y - 2)^2 = 25$$ .

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

Calculate the distance from the point to the center. If it's less than r, inside; equal to r, on; greater than r, outside.

What is the formula for the area of a circle?

The area of a circle is given by $$A = \text{pi} r^2$$ .

If the radius of a circle is doubled, how does the area change?

If the radius is doubled, the area increases by a factor of four, since area is proportional to the square of the radius.

Equations of Circles 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

Back

4.

FLASHCARD QUESTION

Front

How do you calculate the diameter of a circle from its radius?

Back

5.

FLASHCARD QUESTION

Front

What is the relationship between the endpoints of a diameter and the center of a circle?

Back

6.

FLASHCARD QUESTION

Front

Write the equation of a circle with center (0, 0) and radius 4.

Back

7.

FLASHCARD QUESTION

Front

What is the distance formula used to find the radius of a circle?

Back

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