(a)
To find: the equation of the tangent line to the parabola at
(a)
Answer to Problem 10PS
The equation of the tangent line at
Explanation of Solution
Given information:
The equation of parabola is
Calculation:
The slope of the parabola
The derivative of the function
The derivative of the parabola
The slope of the parabola
Therefore, the slope of the parabola
The equation of the tangent line is computed as follows,
Substitute
Therefore, the equation of the tangent line at
(b)
To find: the equation of the normal line to the parabola
(b)
Answer to Problem 10PS
The equation of the normal line at
Explanation of Solution
Calculation:
From part (a), the slope of the tangent line of parabola
Since the normal line is perpendicular to the tangent line, the product of the two slope is
The equation of the normal line is computed as follows,
Substitute
Therefore, the equation of the normal line at
The normal line intersects the parabola other than
Substitute
Solution of the equation
Substitute
Therefore, the normal line intersects the parabola other than
(c)
To find: the equation of the tangent and normal line to the parabola at
(c)
Answer to Problem 10PS
The equation of the tangent line at
Explanation of Solution
Calculation:
The slope of the parabola
The derivative of the function
The derivative of the parabola
The slope of the parabola
Therefore, the slope of the parabola
The equation of the tangent line is computed as follows,
Substitute
Therefore, the equation of the tangent line at
The tangent line of the parabola at
That is, the normal of the parabola at
Chapter 12 Solutions
EBK PRECALCULUS W/LIMITS
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