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To find: an equation of the line.
![Check Mark](/static/check-mark.png)
Answer to Problem 56AYU
Thus, the equation of line is
Explanation of Solution
Given:
The standard form of an equation of a circle is
In order to convert the first equation to standard form, complete the square in both
Subtract
Next, group the expressions involving
In order to complete the squares, take half the coefficients of
Factor the equation.
The equation obtained can be rewritten
On comparing the equation with the standard form, the values obtained are
Thus the center
Similarly, convert the second equation to standard form, complete the square in both
Subtract
Next, group the expressions involving
In order to complete the squares, take half the coefficients of
Factor the equation.
On comparing the equation with the standard form, the values obtained are
Thus the center
In order to find the equation of the line passing through the centers of the two circles, use the point-slope form,
Find the slope
Substitute
Simplify,
Substitute the values of
Thus, the equation of line is
Conclusion:
Thus, the equation of line is
Chapter 1 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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