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CalculusCalculus10th Edition

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Chapter 10.1, Problem 68E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 53E
Problem 51E
Problem 52E
Problem 57E
Problem 58E
Problem 55E
Problem 54E
Problem 63E
Problem 69E
Problem 56E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
Problem 93E
Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Proof

(a) Prove that if any two tangent lines to a parabola intersect at right angles, then their point of intersection must lie on the directrix.

(b) Demonstrate the result of pan (a) by showing that the

tangent lines to the parabola x 2 − 4 x − 4 y + 8 = 0 at the

points ( − 2 , 5 ) and ( 3 , 5 4 ) intersect at right angles and that their point of intersection lies on the directrix.

64.a)

To determine

To Prove: If two tangent lines to a parabola intersect at right angles then the point of intersection must lie on the directrix of parabola.

Explanation

Given: Two lines of a parabola intersect at right angles.

Explanation: Consider the equation of parabola, y=x2.

The slope of the tangent is provided by dydx=2x.

Consider two points on the parabola (x1,y1) and (x2,y2). given by a and b

Therefore, the slope of the tangent lines for both points would be 2x1 and 2x2 respectively.

Therefore, the equation of the tangent lines is,

y−y1=2x1(x−x1) and y−y2=2x2(x−x2)

Solve for y in this case,

y−y1=2x1(x−x1

64b)

To determine
Use the result of the part (a), to show that the tangent lines to the parabola x2−4x−4y+8=0 lies on the equation of directrix.

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In Exercises , a field , a polynomial over , and an element of the field obtained by adjoining a zero of to ...

Elements Of Modern Algebra

Valiant Plumbing ordered sinks from a supplier. The sinks had a net price of $8,300 and terms of sale of 3/15, ...

Contemporary Mathematics for Business & Consumers

limxx3x+2

Calculus: Early Transcendental Functions (MindTap Course List)

Using Formulas In Exercises 77-82, find the indefinite integral by using the appropriate formula from Exercises...

Calculus of a Single Variable

In Exercises 1-8, refer to the following matrices, and perform the indicated operations. Round your answers to ...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 23 to 26, find an equation for each sphere. With center 1,2,3 and containing the point 5,5,3.

Elementary Geometry for College Students

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