56. Use the Greek method described in Problem 55 to find an equation of the tangent line to the circle
at the point .
To find: The equation of the tangent line to the circle.
Answer to Problem 56AYU
Solution:
Explanation of Solution
Given:
at the point
Finding the slope of the radius.
That is to find the center of the circle, we need to rewrite the given equation in its standard form.
The center of this circle is
Slope of the radius = slope of the line joining center
Since the radius and tangent are perpendicular to each other, the product of their slopes must be . We can use this fact to find the slope of the tangent.
Therefore, the slope of the tangent line is
Use the point slope from the line to get the equation of the tangent.
Add on both sides
Therefore, we get
Chapter 1 Solutions
Precalculus Enhanced with Graphing Utilities
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