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To find: an equation of the tangent line.
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Answer to Problem 54AYU
Therefore, the equation of the tangent line is
Explanation of Solution
Given:
U
Since the line containing the center and the tangent line are perpendicular, the product of their slopes will be
Group the terms containing
Complete the square of each expression in parentheses. The numbers added to the left-hand side must be added to the right-hand side also.
Factor the expression.
The standard from of an equation of a circle with radius
It is given that
Substitute for the values
Now, find
The slope
The tangent also has the point
Multiply the numerator and denominator of right-hand side of the equation by
Simplify
Subtract
Therefore, the equation of the tangent line is
Conclusion:
Therefore, the equation of the tangent line is
Chapter 1 Solutions
Precalculus
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
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