Ch 10 Circles

Front

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

Back

(x - h)² + (y - k)² = r²

Front

What is the center of the circle given by the equation (x + 1)² + (y - 3)² = 25?

Back

The center is (-1, 3).

Front

What is the radius of the circle given by the equation (x + 1)² + (y - 3)² = 25?

Back

The radius is 5 (since r² = 25, r = √25 = 5).

Front

How do you find the length of an arc in a circle?

Back

Arc length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.

Front

What is the measure of a full circle in degrees?

Back

360°.

Front

If the measure of arc GE is 120°, what fraction of the circle does it represent?

Back

120°/360° = 1/3 of the circle.

Front

What is the relationship between the central angle and the arc length?

Back

The central angle in degrees is proportional to the arc length.

Front

What is the formula to find the area of a circle?

Back

Area = πr².

Front

If a circle has a radius of 4, what is its area?

Back

Area = π(4)² = 16π.

Front

What is the distance formula used to find the radius of a circle given a point on the circle and the center?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).