Question

The equation of a circle in a Cartesian coordinate system is given by ( (x - h)² + (y - k)² = r² ), where ((h, k)) represents the center of the circle and (r) is the radius.

A) True
B) False

Answer 1

The equation ((x - h)² + (y - k)² = r²) correctly represents a circle in a Cartesian coordinate system where (h, k) is the center and r is the radius, and this is true.

Step-by-step explanation:

The statement regarding the equation of a circle being ((x - h)² + (y - k)² = r²), where ((h, k)) is the center and (r) is the radius, is True. A circle is a special type of ellipse where the two foci coincide at a single point which is the center of the circle. Therefore, every point on the circumference of the circle is equidistant from the center, defining a radius (r). As such, when you plug any point ((x, y)) on the circumference into the equation, the resulting expression will always equal to the radius squared, confirming that the point lies on the circle.