Which of the following circles lie completely within the fourth quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x - 2)2 + (y + 7)2 = 64C.(x - 12)2 + (y + 0)2 = 72D.(x - 9)2 + (y + 9)2 = 16SUBMITarrow_backPREVIOUS
Question
Which of the following circles lie completely within the fourth quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x - 2)2 + (y + 7)2 = 64C.(x - 12)2 + (y + 0)2 = 72D.(x - 9)2 + (y + 9)2 = 16SUBMITarrow_backPREVIOUS
Solution
The equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
The fourth quadrant is where x > 0 and y < 0.
A. The center of the circle is (5, -5) and the radius is √9 = 3. The circle will extend 3 units in all directions from the center. So, the circle will extend to y = -2 and x = 8. This circle lies completely within the fourth quadrant.
B. The center of the circle is (2, -7) and the radius is √64 = 8. The circle will extend 8 units in all directions from the center. So, the circle will extend to y = 1 and x = 10. This circle does not lie completely within the fourth quadrant.
C. The center of the circle is (12, 0) and the radius is √72 ≈ 8.48. The circle will extend 8.48 units in all directions from the center. So, the circle will extend to y = 8.48 and x = 20.48. This circle does not lie completely within the fourth quadrant.
D. The center of the circle is (9, -9) and the radius is √16 = 4. The circle will extend 4 units in all directions from the center. So, the circle will extend to y = -5 and x = 13. This circle lies completely within the fourth quadrant.
So, the circles that lie completely within the fourth quadrant are A and D.
Similar Questions
Which of the following circles have their centers in the second quadrant?Check all that apply.A.(x - 5)2 + (y + 5)2 = 9B.(x + 3)2 + (y - 2)2 = 8C.(x + 12)2 + (y - 9)2 = 19D.(x - 2)2 + (y + 7)2 = 64SUBMITarrow_backPREVIOUS
Which of the following circles have their centers on the y-axis?Check all that apply.A.(x - 0)2 + (y + 5)2 = 74B.(x - 0)2 + (y - 0)2 = 44C.(x - 4)2 + (y - 0)2 = 22D.(x + 1)2 + (y - 7)2 = 16SUBMITarrow_backPREVIOUS
Which of the following circles have their centers on the x-axis?Check all that apply.
Write the equation of a circle whose center is (-9, -8) and which has a radius of 5.A. left parenthesis x plus 9 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 10B. left parenthesis x minus 9 right parenthesis squared plus left parenthesis y minus 8 right parenthesis squared equals 25C. left parenthesis x plus 9 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 5D. left parenthesis x plus 9 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 25
Which of the following points lies outside the circle with center (0,0) and radius 5 ?A.(4.1, 1)B.(4, 2)C.(3.8, 3)D.(2, 5)
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