A line that is tangent to a circle touches the circle at just one point and is perpendicular to a radius at that point. First, we find the slope of the radius inside the circle from the center to the point of tangency. Then, since we seek a line perpendicular to this, we use the opposite sign reciprocal slope with the point of tangency to write the new line equation. Tangent lines like this will be a key idea in your study of calculus.
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