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Example Questions
Example Question #71 : Functions And Graphs
Note: Figure NOT drawn to scale.
Refer to the above figure. The circle has its center at the origin; the line is tangent to the circle at the point indicated. What is the equation of the line in slope-intercept form?
Possible Answers:
Insufficient information is given to determine the equation of the line.
Correct answer:
Explanation:
A line tangent to a circle at a given point is perpendicular to the radius from the center to that point. That radius, which has endpoints , has slope
.
The line, being perpendicular to this radius, will have slope equal to the opposite of the reciprocal of that of the radius. This slope will be . Since it includes point , we can use the point-slope form of the line to find its equation:
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