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In the standard (x,y)(x,y) coordinate plane, a circle with its center at (8,5)(8,5) and a radius of 99 coordinate units has which of the following equations?\newlineF. (x8)2+(y5)2=81(x-8)^{2}+(y-5)^{2}=81\newlineG. (x8)2+(y5)2=9(x-8)^{2}+(y-5)^{2}=9\newlineH. (x+8)2+(y+5)2=81(x+8)^{2}+(y+5)^{2}=81\newlineJ. (x+8)2+(y+5)2=9(x+8)^{2}+(y+5)^{2}=9\newlineK. (x+5)2+(y+8)2=81(x+5)^{2}+(y+8)^{2}=81

Full solution

Q. In the standard (x,y)(x,y) coordinate plane, a circle with its center at (8,5)(8,5) and a radius of 99 coordinate units has which of the following equations?\newlineF. (x8)2+(y5)2=81(x-8)^{2}+(y-5)^{2}=81\newlineG. (x8)2+(y5)2=9(x-8)^{2}+(y-5)^{2}=9\newlineH. (x+8)2+(y+5)2=81(x+8)^{2}+(y+5)^{2}=81\newlineJ. (x+8)2+(y+5)2=9(x+8)^{2}+(y+5)^{2}=9\newlineK. (x+5)2+(y+8)2=81(x+5)^{2}+(y+8)^{2}=81
  1. Identify Circle Equation Formula: The equation of a circle in the standard (x,y)(x,y) coordinate plane with center at (h,k)(h,k) and radius rr is given by the formula (xh)2+(yk)2=r2(x-h)^2 + (y-k)^2 = r^2. We need to plug in the values of hh, kk, and rr into this formula to find the equation of the circle.
  2. Determine Center and Radius: The center of the circle is given as (8,5)(8,5), so h=8h = 8 and k=5k = 5. The radius of the circle is given as 99 units, so r=9r = 9.
  3. Substitute Values into Formula: Now we will substitute h=8h = 8, k=5k = 5, and r=9r = 9 into the circle equation formula. This gives us (x8)2+(y5)2=92(x-8)^2 + (y-5)^2 = 9^2.
  4. Calculate Radius Squared: Next, we calculate 929^2 to find the value that will be on the right side of the equation. 929^2 equals 8181.
  5. Final Equation of Circle: After substitifying the values and calculating the square of the radius, we get the equation of the circle as (x8)2+(y5)2=81(x-8)^2 + (y-5)^2 = 81.

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