Bluebook SAT Test Circles 2

Question 1

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

Accepted Answer

(x + 2)² + (y − 4)² = 9

Answer

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

Question 2

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

Accepted Answer

135°

Answer

(3π/4) × (180°/π) = 3 × 45° = 135°.

Question 3

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

Accepted Answer

9

Answer

C = 2πr → 18π = 2πr → r = 9.

Question 4

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

Accepted Answer

4π

Answer

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

Question 5

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

Accepted Answer

2

Answer

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

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