In Exercises 99-102, find an equation of the tangent line to...

In Exercises $99-102,$ find an equation of the tangent line to the circle at the indicated point. Recall from geometry that the tangent line to a circle is perpendicular to the radius of the circle at the point of tangency.
$$
x^{2}+y^{2}=169 \quad(-5,12)
$$

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Key Concepts

Point-Slope Form

The point-slope form of a line, given by the equation y - y? = m(x - x?), is a useful tool for writing the equation of a line when a point on the line and its slope are known. This form is particularly helpful when finding the equation of a tangent line to a circle at a specific point.

Perpendicular Slopes

When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other. This relationship is commonly used in coordinate geometry to determine the slope of a tangent line given the slope of the radius at the point of tangency.

Tangent Line

A tangent line to a circle is a line that touches the circle at exactly one point. At the point of tangency, the tangent line is perpendicular to the radius drawn to that point, a property that is critical in solving problems involving tangents to circles.

Circle

A circle is the set of all points in a plane that are a fixed distance (the radius) from a given point (the center). Its standard equation, such as x² + y² = r², represents this geometric relationship and is a fundamental element in analytic geometry.

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