Concept explainers
Proof Prove Theorem 10.4 by showing that the tangent line to an ellipse at a point P makes equal angles with lines through P and the foci (see figure). [Hint: (1) Find the slope of the tangent line at P, (2) find the slopes of the lines through P and each focus, and (3) use the formula for the tangent of the angle
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Chapter 10 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
- Tangent lines Find an equation of the line tangent to the cycloidx = t - sin t, y = 1 - cos t at the points corresponding to t = π/6 and t = 2π/3.arrow_forwardTangent lines Carry out the following steps.a. Verify that the given point lies on the curve.b. Determine an equation of the line tangent to the curve at the given point.arrow_forwardPart i PARAMETRIC EQUATION: find the second derivative y with respect to x from the parametric equations given. plot the curve and draw the tangent line and locate the point of tangency.arrow_forward
- Slope of a Curve at a PointIn Exercises 7–18, use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.arrow_forwardSlopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points.arrow_forwardUsing parametric equations, find all points at which the following curves have the given slope.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning