Explanation Given info. Two given planes are z = x 2 − y 2 z = x 2 + x y − 1 Concept used: Intersection of a planes can be find out by find the value of x and y with the help to given two equation. Then replace one variable with the parameter. Calculation: z = x 2 − y 2 → ( 1 ) z = x 2 + x y − 1 → ( 2 ) From equation ( 1 ) and ( 2 ) you get x 2 − y 2 = x 2 + x y − 1 x y = 1 − y 2 x = 1 − y 2 y x = 1 y − y x = y − 1 − 1 Find the value of z in the form of y. z = x 2 + x y − 1 = ( put x = y 2 − y ) = ( y − 1 − y ) 2 + ( y − 1 − y ) y − 1 ( simplify ( a − b ) 2 = a 2 + b 2 − 2 a b ) = ( y − 1 ) 2 + ( y ) 2 − 2...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 14.1, Problem 46E

To determine

Find a parameterization of the curve formed buy the surfaces.

$z = x^{2} - y^{2} and z = x^{2} + x y - 1$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 45E

Chapter 14.1, Problem 47E

Students have asked these similar questions

In Exercises 31-36, find a parametrization of the tangent line at the point indicated. (lns)i + s- 1 j + 9sk, s = 1

Find a parametrization of the paraboloid given by f (x, y) = x 2 + y2.

Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find a parameterization of the curve formed buy the surfaces. z = x 2 − y 2 and z = x 2 + x y − 1

Solution Summary: The author explains how to determine a parameterization of the curve formed buy the surfaces. Intersection of planes can be found by finding the value of x and y with the help of two equations.

Concept explainers

Videos

Find a parameterization of the curve formed buy the surfaces.

$z = x^{2} - y^{2} and z = x^{2} + x y - 1$

Want to see the full answer?

Chapter 14 Solutions

Find a parameterization of the curve formed buy the surfaces. z = x 2 − y 2 and z = x 2 + x y − 1

Solution Summary: The author explains how to determine a parameterization of the curve formed buy the surfaces. Intersection of planes can be found by finding the value of x and y with the help of two equations.

Concept explainers

Videos

Find a parameterization of the curve formed buy the surfaces. z=x2−y2 and z=x2+xy−1

Want to see the full answer?

Chapter 14 Solutions

Find a parameterization of the curve formed buy the surfaces.

$z = x^{2} - y^{2} and z = x^{2} + x y - 1$