Question

Write an equation that describes the position and range of each circle.

A) (x² + y² = r²)
B) (y = mx + b)
C) (x = h) and (y = k) for a circle centered at ((h, k))
D) (y = a(x - h)² + k) for a circle centered at ((h, k))

Answer 1

The equation that describes the position and range of each circle is (y = a(x - h)² + k) for a circle centered at (h, k).

Step-by-step explanation:

The equation that describes the position and range of each circle is option D) (y = a(x - h)² + k) for a circle centered at ((h, k)).

This equation represents a vertical parabola with the vertex at the point (h, k), which is the center of the circle. The 'a' value determines the opening direction and width of the parabola. By substituting different values for 'a' and adjusting the coefficients, you can create various circles in the coordinate system.

For example, if 'a' is positive, the parabola opens upwards, creating a circle above the vertex. If 'a' is negative, the parabola opens downwards, creating a circle below the vertex.