Answer:
B and C
Explanation:
Coordinates of A: (5,-5), which is in the 4th quadrant.
Coordinates of B: (-12,9), which is in the 2nd quadrant.
Coordinates of C: (-3,2), which is in the 2nd quadrant.
Coordinates of D: (2,-7), which is in the 4th quadrant.
The circles have their centers in the second quadrant are : [tex](x+12)^2+(y-9)^2=19[/tex] and [tex](x+3)^2+(y-2)^2=8[/tex]
The correct answers are option (B) and option (C)
"An equation of circle with center (h, k) and radius r is [tex](x-h)^2+(y-k)^2=r^2[/tex] "
For given question,
We have been given the equations of the circles.
We find the center of each circle.
We know that the coordinates of any point in the second quadrant are of the form (-x, y)
The x-coordinate must be negative and Y-coordinate must be positive.
A.
[tex](x-5)^2+(y+5)^2=9\\\\(x-5)^2+(y+5)^2=3^2[/tex]
By comparing above equation of circle with [tex](x-h)^2+(y-k)^2=r^2[/tex] we have the center = (5, -5) and the radius = 3
The center of the circle lies in the fourth quadrant.
B.
[tex](x+12)^2+(y-9)^2=19\\\\(x+12)^2+(y-9)^2=(\sqrt{19} )^2[/tex]
By comparing above equation of circle with [tex](x-h)^2+(y-k)^2=r^2[/tex] we have the center = (-12, 9) and the radius = [tex]\sqrt{19}[/tex]
The center of the circle lies in the second quadrant.
C.
[tex](x+3)^2+(y-2)^2=8\\\\(x+3)^2+(y-2)^2=(2\sqrt{2} )^2[/tex]
By comparing above equation of circle with [tex](x-h)^2+(y-k)^2=r^2[/tex] we have the center = (-3, 2) and the radius = [tex]2\sqrt{2}[/tex]
The center of the circle lies in the second quadrant.
D.
[tex](x-2)^2+(y+7)^2=64\\\\(x-2)^2+(y+7)^2=8^2[/tex]
By comparing above equation of circle with [tex](x-h)^2+(y-k)^2=r^2[/tex] we have the center = (2, -7) and the radius = 8
The center of the circle lies in the fourth quadrant.
Therefore, the circles have their centers in the second quadrant are : [tex](x+12)^2+(y-9)^2=19[/tex] and [tex](x+3)^2+(y-2)^2=8[/tex]
The correct answers are option (B) and option (C)
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