Find an equation of the circle that satisfies the given conditions. Center at the origin; passes through (1,6)

x² + y² = 37

The equation of a circle centred at the origin is.

x² + y² = r² (where r is the radius)

The radius can be calculated using the distance formula

r = √ (x₂ - x₁) ² + (y₂ - y₁) ²

where (x₁, y₁) = (0,0) and (x₂, y₂) = (1,6)

r = √ (1 - 0) ² + (6 - 0) ² = √1 + 36 = √37⇒ r² = (√37) ² = 37

x² + y² = 37 is the equation of the circle