Question

Calculate the standard form of a circle with endpoints of a diameter.

a) (x - h)² + (y - k)² = r²
b) (x + h)² + (y + k)² = r²
c) x² + y² = r²
d) x² - y² = r²

Answer 1

The correct standard form of a circle given endpoints of a diameter is a) (x - h)² + (y - k)² = r², where (h, k) is the circle's center and r is the radius.

Step-by-step explanation:

To calculate the standard form of a circle from endpoints of a diameter, we use the formula (x - h)² + (y - k)² = r² where (h, k) is the center of the circle, and r is the radius. The standard form of the equation of a circle is always written with squared terms and equal to the radius squared. First, we need to find the midpoint of the diameter which gives us the coordinates (h, k) for the center. Then, using the endpoints of the diameter, we calculate the distance between them to find the diameter; half of this distance will be our radius (r). The correct standard form from the given options is a) (x - h)² + (y - k)² = r².