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Concept explainers
(a)
To show that
(a)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given information:
The equation of circle is
Concept Used:
- The tangent line to a circle is the line that intersects the circle at a single point, which is known as point of tangency.
Calculation:
Consider the equation of the circle,
And the equation of the tangent line
Substitute the value of y from ( ii ) into ( i ) and simplify further as shown below,
Now solve it using the
Substitute this value of x in ( iii ) to get
It implies that
(b)
To show that
(b)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given information:
The equation of circle is
Concept Used:
- The tangent line to a circle is the line that intersects the circle at a single point, which is known as point of tangency.
Calculation:
The x -coordinate of the point of tangency is given by
From the relation found in part (a), substitute
Substitute this value of x in the equation of tangent and simplify further to get
Thus, the point of tangency is
(c)
To show that
(c)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given information:
The equation of circle is
Concept Used:
- The tangent line to a circle is the line that intersects the circle at a single point, which is known as point of tangency.
Calculation:
Observe that the center of the circle is at origin (0, 0). So, the slope of the equation of the line connecting the center (0, 0) and the point of tangency
Also observe that the slope of the tangent line is m .
Since the slope of the line connecting to the center and point of tangency is negative reciprocal of the slope of the tangent line, so both the lines are perpendicular.
Thus, the tangent line is perpendicular to the line containing the center of the circle and the point of tangency.
Chapter 1 Solutions
Precalculus
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (4th Edition)
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Precalculus (10th Edition)
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