Conic - Circle Unit 4 Review

Front

In the equation (x+3)²+(y-2)²=4, what is the center of the circle?

Back

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

Front

What is the standard form of a circle's equation?

Back

The standard form is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

Determine the center and radius of the circle given by the equation: x² + y² + 10x - 8y - 8 = 0.

Back

Center C = (-5, 4), Radius r = 7.

Front

In the equation (x-3)²+(y-2)²=16, what is the radius of the circle?

Back

The radius of the circle is 4 (since r² = 16).

Front

What does the term 'radius' refer to in a circle?

Back

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

Front

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

Back

The center (h, k) can be found directly from the equation (x-h)² + (y-k)² = r².

Front

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

Back

The diameter is twice the radius (d = 2r).

Front

If the center of a circle is at (2, -3) and the radius is 5, what is the equation of the circle?

Back

The equation is (x-2)² + (y+3)² = 25.

Front

What is the effect of changing the value of 'h' in the equation (x-h)² + (y-k)² = r²?

Back

Changing 'h' shifts the circle left or right along the x-axis.

Front

What does the term 'circumference' refer to in relation to a circle?

Back

The circumference is the distance around the circle, calculated as C = 2πr.