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A circle in the 
xy-plane has the equation

(x-4)^(2)+(y+1)^(2)=16. Which of the following points does NOT lie inside the circle?
Choose 1 answer:
(A) 
(7,-3)
(B) 
(4,-1)
(C) 
(2,2)
(D) 
(0,0)

A circle in the \newlinexyxy-plane has the equation\newline(x4)2+(y+1)2=16(x-4)^{2}+(y+1)^{2}=16. Which of the following points does NOT lie inside the circle?\newlineChoose 11 answer:\newline(A) \newline(7,3)(7,-3)\newline(B) \newline(4,1)(4,-1)\newline(C) \newline(2,2)(2,2)\newline(D) \newline(0,0)(0,0)

Full solution

Q. A circle in the \newlinexyxy-plane has the equation\newline(x4)2+(y+1)2=16(x-4)^{2}+(y+1)^{2}=16. Which of the following points does NOT lie inside the circle?\newlineChoose 11 answer:\newline(A) \newline(7,3)(7,-3)\newline(B) \newline(4,1)(4,-1)\newline(C) \newline(2,2)(2,2)\newline(D) \newline(0,0)(0,0)
  1. Circle Equation Explanation: The equation of the circle is given by (x4)2+(y+1)2=16(x-4)^2 + (y+1)^2 = 16. The center of the circle is at the point (4,1)(4, -1) and the radius is the square root of 1616, which is 44.
  2. Point Inside Circle Check: To determine if a point lies inside the circle, we can plug the coordinates of the point into the circle's equation and see if the resulting value is less than 1616. If it is, the point lies inside the circle; if it is equal to 1616, the point lies on the circle; and if it is greater than 1616, the point lies outside the circle.
  3. Point A Check: Let's check point (A)(7,3)(A) (7, -3). Substitute x=7x = 7 and y=3y = -3 into the circle's equation: (74)2+(3+1)2=32+(2)2=9+4=13(7-4)^2 + (-3+1)^2 = 3^2 + (-2)^2 = 9 + 4 = 13. Since 1313 is less than 1616, point (A)(A) lies inside the circle.
  4. Point B Check: Now let's check point (B)(4,1)(B) (4, -1). Substitute x=4x = 4 and y=1y = -1 into the circle's equation: (44)2+(1+1)2=02+02=0(4-4)^2 + (-1+1)^2 = 0^2 + 0^2 = 0. Since 00 is less than 1616, point (B)(B) lies inside the circle.
  5. Point C Check: Next, let's check point (C)(2,2)(C) (2, 2). Substitute x=2x = 2 and y=2y = 2 into the circle's equation: (24)2+(2+1)2=(2)2+32=4+9=13(2-4)^2 + (2+1)^2 = (-2)^2 + 3^2 = 4 + 9 = 13. Since 1313 is less than 1616, point (C)(C) lies inside the circle.
  6. Point D Check: Finally, let's check point (D) (0,0)(0, 0). Substitute x=0x = 0 and y=0y = 0 into the circle's equation: (04)2+(0+1)2=(4)2+12=16+1=17(0-4)^2 + (0+1)^2 = (-4)^2 + 1^2 = 16 + 1 = 17. Since 1717 is greater than 1616, point (D) does NOT lie inside the circle.

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