Circles Flashcards

Which equation represents a circle with center (−2, 4) and radius 3?

Answer: (x + 2)² + (y − 4)² = 9

Center (−2, 4) and r = 3: (x − (−2))² + (y − 4)² = 3² gives (x + 2)² + (y − 4)² = 9.

Convert the central angle 3π/4 radians to degrees.

Answer: 135°

(3π/4) × (180°/π) = 3 × 45° = 135°.

A circle has circumference 18π. What is its radius?

Answer: 9

C = 2πr → 18π = 2πr → r = 9.

Two radii of a circle form a central angle of 60°. The radius is 12. What is the length of the arc between them?

Answer: 4π

Arc = (60/360)(2π·12) = (1/6)(24π) = 4π.

The equation x² + y² + 6x − 2y + 6 = 0 can be rewritten in standard form. What is the radius?

Answer: 2

Complete the square: (x²+6x+9)+(y²−2y+1) = −6+9+1 = 4; so (x+3)²+(y−1)²=4, radius = 2.

A chord in a circle has a length equal to the radius. What is the central angle subtended by this chord?

Answer: 60°

When chord length = radius, the triangle formed by the two radii and the chord is equilateral, giving a central angle of 60°.

A sector of a circle has radius 8 and area 16π. What is the central angle in degrees?

Answer: 90°

16π = (θ/360°)·π(64) → θ/360° = 16π/64π = 1/4 → θ = 90°.