Question

A circle has a center at (3,5). If point A(5,2) lies on the circle, which of the following is the slope of the tangent line to circle C at point A?

1. 3/2
2. 2/3
3. -3/2
4. -2/3

Answer 1

• 2. 2/3

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We know the tangent is perpendicular to radius.

Find the slope of the radius using its endpoints:

• slope(radius) = (2 - 5)/(5 - 3) = - 3/2

Perpendicular lines have negative reciprocal slopes, therefore the slope of the tangent is:

• slope(tangent) = - 1 / ( - 3/2) = 2/3

The matching choice is 2.