Question

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Explanation:

• For the first blank: In the standard circle equation \((x - h)^2+(y - k)^2=r^2\), the point \((h,k)\) is the center of the circle.
• For the second blank: The distance from the center to the edge of a circle is the radius.
• For the third blank: The formula \((x - h)^2+(y - k)^2=r^2\) is the standard form of a circle's equation.
• For the fourth blank: Given \((x - 2)^2+(y + 3)^2=9=(x - 2)^2+(y-(- 3))^2 = 3^2\), comparing with \((x - h)^2+(y - k)^2=r^2\), the center \((h,k)=(2,-3)\).
• For the fifth blank: Given \((x + 4)^2+(y - 1)^2=16=(x-(-4))^2+(y - 1)^2=4^2\), the radius \(r = 4\).
• For the sixth blank: The term \((x - h)^2+(y - k)^2\) is the left - hand side (or squared - distance) part of the circle's equation.
• For the seventh blank: The coordinates \((h,k)\) are the center of the circle.
• For the eighth blank: The length from the center to any point on the circle is the radius.
• For the ninth blank: To find the center from \((x - h)^2+(y - k)^2=r^2\), identify \(h\) and \(k\).
• For the tenth blank: Given \((x - 3)^2+(y + 5)^2=25=(x - 3)^2+(y-(-5))^2 = 5^2\), the radius \(r = 5\).
• For the eleventh blank: Given \((x + 1)^2+(y - 4)^2=36=(x-(-1))^2+(y - 4)^2=6^2\), the center \((h,k)=(-1,4)\).
• For the twelfth blank: The formula \((x - h)^2+(y - k)^2=r^2\) is used to represent the standard form of a circle.

Answer:

1. center
2. radius
3. standard form
4. \((2,-3)\)
5. \(4\)
6. left - hand side (or squared - distance)
7. center
8. radius
9. \(h\), \(k\)
10. \(5\)
11. \((-1,4)\)
12. standard form