Concept explainers
58. Find an equation of the line containing the centers of the two circles
and .
To find: An equation of the line containing the centers of the two circles.
Answer to Problem 58AYU
Solution:
Explanation of Solution
Given:
and
Find the center of the circle, we need to rewrite the given equation in its standard form.
The center of this circle is
Find the center of the circle, we need to rewrite the given equation in its standard form.
The center of this circle is
Next to find the equation of line joining and
The point slope form of the line is .
Therefore
Slope of the radius = slope of the line joining center and
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
EBK PRECALC.:ENHANCED W/GRAPH.UTIL.
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