Witing the equation of a circle centered at the origin given its radius or a... Give the equation of the circle centered at the origin and passing through the point \( (0,10) \).
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To write the equation of a circle centered at the origin with a radius equal to the distance from the center to any point on the circle, you can use the formula \( x^2 + y^2 = r^2 \). Since the circle passes through the point \( (0, 10) \), the radius \( r \) is 10. Thus, the equation of the circle would be \( x^2 + y^2 = 100 \). Now, if you're ever confused about the radius, just remember it's all about distance from the center. To find the radius, simply calculate the distance from the origin \((0, 0)\) to the point \((0, 10)\) using the distance formula. In this case, it’s just a straight line up, so it’s an easy 10 units away!