Equations for Tangent Lines to Circles
A circle of radius 5 passes through points 𝐴(−3, 3) and 𝐵(3, 1).
a. What is the special name for segment 𝐴𝐵?
b. How many circles can be drawn that meet the given criteria? Explain how you know.
c. What is the slope of 𝐴𝐵?
d. Find the midpoint of 𝐴𝐵.
e. Find the equation of the line containing a diameter of the given circle perpendicular to 𝐴𝐵.
f. Is there more than one answer possible for part (e)?
Consider the circle with equation (𝑥 − 3)2 + (𝑦 − 5)2 = 20. Find the equations of two tangent lines to the circle that each has slope 1/2.
Refer to the diagram below.
Let 𝑝 > 1. What is the equation of the tangent line to the circle 𝑥2 + 𝑦2 = 1 through the point (𝑝, 0) on the 𝑥-axis with a point of tangency in the upper half-plane?
A tangent line to a circle is perpendicular to the radius of the circle drawn to the point of tangency.
TANGENT TO A CIRCLE: A tangent line to a circle is a line in the same plane that intersects the circle in one and only one point. This point is called the point of tangency.
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