write the equation in standard form for the circle passing through (6,8) centered at the origin

Answer 1

The standard form for a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Since the radius is not given, we need to plug in the information given. Since the center is at the origin, this is the point (0, 0). Since another point on the circle is (6, 8), that is the (x, y) value. So let's plug it into the equation:

(6 - 0)² + (8 - 0)² = r² --> 6² + 8² = r² --> 100 = r² --> 10 = r.

Since r = 10 and the center is (0, 0), the standard form equation of this circle is (x - 0)² + (y - 0)² = 10² or just x² + y² = 100.

I hope this helps!