Concept explainers
a.
Toprove:That the tangent to the ellipse
a.
Explanation of Solution
Given information:The ellipse is
Formula used:
Two-point form of line is
Also product, quotient and chain rule of derivatives are used.
Proof:
The ellipse is
Subtract equation (1) from equation (2)
The equation for the line AB in two-point form is:
By using the result of equation (3) in equation (4)
The line AB becomes tangent to ellipse, if
Then
Put equation (6) in equation (5), we get
Here
Hence proved that the tangent to the ellipse
b.
To calculate:The equation of tangent to the hyperbola
b.
Answer to Problem 65E
The tangent to the hyperbola
Explanation of Solution
Given information:The hyperbola is
Formula used:
Two-point form of line is
Also product, quotient and chain rule of derivatives are used.
Calculation:
The hyperbola is
Subtract equation (1) from equation (2)
The equation for the line AB in two-point form is:
By using the result of equation (3) in equation (4)
The line AB becomes tangent to hyperbola, if
Then
Put equation (6) in equation (5), we get
Here
Hence the tangent to the hyperbola
Chapter 4 Solutions
Calculus: Graphical, Numerical, Algebraic
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