To find: The equation of the tangent line to the parabola at the given point.
Answer to Problem 59E
The equation of the tangent is
Explanation of Solution
Given information:
The equation of the parabola is,
The given point is
Concept used:
Write the standard equation of a parabola along the vertical axis.
For this equation, the focus is at
Write the standard equation of a parabola along the horizontal axis.
For this equation, the focus is at
The equation of the parabola is,
The value of
The distance between the focus and the given point is calculated as,
The distance between the focus and the point of the tangent at y-intercept is calculated as,
The slope of the tangent line is calculated as,
The equation of the tangent is written as,
Thus, the equation of the tangent is
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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