SAT Circles Practice Question 8 (Hard)

Math · Geometry and TrigonometryHard

In the $xy$ -plane, a circle has center $(3, 4)$ , and the point $(6, 8)$ lies on the circle. What is the slope of the line tangent to the circle at $(6, 8)$ ?

$-\frac{3}{4}$

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{3}{4}$

Show answer and explanation

Answer: A

A tangent line is perpendicular to the radius at the point of tangency. The slope of the radius from $(3, 4)$ to $(6, 8)$ is $\frac{8 - 4}{6 - 3} = \frac{4}{3}$ . The perpendicular slope is the negative reciprocal, $-\frac{3}{4}$ .

Choice B is the slope of the radius itself, not the tangent line.

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