Question

the point (h, k) in the circles equation (x - h)^2+(y - k)^2=r^2 is known as the

the distance from the center to the edge of the circle is called the

the formula (x - h)^2+(y - k)^2=r^2 represents the of a circle.

in the equation (x - 2)^2+(y + 3)^2=9, the center of the circle is

the radius of the circle in the equation (x + 4)^2+(y - 1)^2=16 is

the term (x - h)^2+(y - k)^2 is known as the part of the circles equation.

the coordinates (h, k) are referred to as the of the circle.

Explanation:

1. In the circle - equation \((x - h)^2+(y - k)^2=r^2\), the point \((h,k)\) represents the center of the circle.
2. The distance from the center to the edge of a circle is the radius.
3. The formula \((x - h)^2+(y - k)^2=r^2\) is the standard - form equation of a circle.
4. For the equation \((x - 2)^2+(y + 3)^2=9\), comparing with \((x - h)^2+(y - k)^2=r^2\), the center is \((2,-3)\) (since \(h = 2\) and \(k=-3\)).
5. For the equation \((x + 4)^2+(y - 1)^2=16\), since \(r^2 = 16\), then \(r = 4\) (taking the positive square - root as radius is a non - negative quantity).
6. \((x - h)^2+(y - k)^2\) is the left - hand side part of the circle's equation.
7. The coordinates \((h,k)\) are the center coordinates of the circle.

Answer:

1. Center
2. Radius
3. Standard - form equation
4. \((2,-3)\)
5. \(4\)
6. Left - hand side
7. Center coordinates