To determine: The equations for the lines that are tangent to the cardioids at the points where it crosses the x -axis.
Answer to Problem 26RE
The required equations are
Explanation of Solution
Given information:
The equation cardioid:
Formula used:
Product rule of differentiation:
Calculation:
The given equation is
The equation shows that the equation of the cardioids crosses the x -axis at the points where
The above are the points where
It is seen that in polar coordinate system if
Rewrite the coordinates as:
Here, the polar curves lie in the xy -plane. This means the slope of the polar curve and the sloe of the tangent line are same.
So,
For
For
Hence, the required equations are
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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