In the standard (x,y) coordinate plane, a circle with its center at (8,5) and a radius of 9 coordinate units has which of the following equations?F. (x−8)2+(y−5)2=81G. (x−8)2+(y−5)2=9H. (x+8)2+(y+5)2=81J. (x+8)2+(y+5)2=9K. (x+5)2+(y+8)2=81
Q. In the standard (x,y) coordinate plane, a circle with its center at (8,5) and a radius of 9 coordinate units has which of the following equations?F. (x−8)2+(y−5)2=81G. (x−8)2+(y−5)2=9H. (x+8)2+(y+5)2=81J. (x+8)2+(y+5)2=9K. (x+5)2+(y+8)2=81
Identify Circle Equation Formula: The equation of a circle in the standard (x,y) coordinate plane with center at (h,k) and radius r is given by the formula (x−h)2+(y−k)2=r2. We need to plug in the values of h, k, and r into this formula to find the equation of the circle.
Determine Center and Radius: The center of the circle is given as (8,5), so h=8 and k=5. The radius of the circle is given as 9 units, so r=9.
Substitute Values into Formula: Now we will substitute h=8, k=5, and r=9 into the circle equation formula. This gives us (x−8)2+(y−5)2=92.
Calculate Radius Squared: Next, we calculate 92 to find the value that will be on the right side of the equation. 92 equals 81.
Final Equation of Circle: After substitifying the values and calculating the square of the radius, we get the equation of the circle as (x−8)2+(y−5)2=81.