Question

Write the equation in standard form for the circle that has a diameter with endpoints (3,8) and (3,–8)

Answer 1

• (x - 3)² + y² = 8²

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Standard form for the equation of a circle is:

• (x − h)² + (y − k)² = r², where the center is (h, k) and the radius is r units

Using the given endpoints of the diameter find the center, which is the midpoint:

• h = 3, as x-coordinate of both endpoints,
• k = 0, as the sum of y-coordinates of endpoints.

The radius is half the distance between endpoints:

• r = (8 - (-8))/2 = 16/2 = 8

Substitute values into equation:

• (x - 3)² + (y - 0)² = 8²
• (x - 3)² + y² = 8²