IGNOU MTE 8 2018 - Find the surface which is orthogonal to the one parameter system z = c

Question

Find the surface which is orthogonal to the one parameter system z = cxy(x² + y²) and which passes through the hyperbola x² - y² = a², z = 0 .

13 Feb 2018

Answer :

Word Count : 486

To find the surface orthogonal to the one-parameter system given by the equation \( z = cxy(x^2 + y^2) \) that passes through the hyperbola \( x^2 - y^2 = a^2 \) and \( z = 0 \), we need to solve for the appropriate surface equation. ### Step 1: Determine the vector normal to the given surface The surface is described by \( z = cxy(x^2 + y^2) \). The gradient of the surface at any point \( (x, y, z) \) will give us the normal vector to the surface. To find the gradient, we first calculate the partial derivatives of \( z \) with respect to \( x \) and \( y \): \[ z = cxy(x^2 + y^2) \] #### Partial derivative with respect to \( x \): \[ \frac{\partial z}{\partial x} = c \left[ y(x^2 + y^2) + x \cdot 2x \cdot y \right] = c y(x^2 + y^2 + 2x^2) \] \[ \frac{\partial z}{\partial x} = c y(3x^2 + y^2) \] #### Partial derivative with respect to \( y \): \[ \frac{\partial z}{\partial y} = c \left[ x(x^2 +

_________ ____ ___ _____ ________.
___ ________ ________ ________ _______.
__________ ________ ___ _____ _________ _______.
_____ _______ ___ _______ ________ _______ _____ _____ _________ __________.
_______ _____ ___ _______ ________ __________ ____.
_____ ___ _______ ________ ________ _________.
_____ __________ ___ _____ ________ ___ __________.
_______ __________ ______ ____ ____ ____ _____ ___ _____ ________ _____ ______.
________ _____ ______ ______ _______ __________ ____ ______ ______ ________ _______.
____ ___ ________ _______ ____ __________ ____ _____ _____.
_____ ___ __________ _______ ____ _____ ________ _____ ________.
___ _______ __________ _______ ____ _______.
________ ________ _______ ___ _______.
____ _____ _______ _____ _________.
_____ ___ ____ _____ _____ ______ _____ ______ ________ __________ _________ ______.
________ _____ _________ _____ ________ __________ ___ ____.
__________ ________ ____ ______ __________ ___ ________ _____.
_____ _______ ____ ___ _________ ________ _______ ______ ____ _______ ___ __________.
_______ _________ _____ ___ _________ ______ ________.
_____ ____ _________ ____ ___ ____ _____ ___ ________ _________.
_________ _______ _________ _______ _____ __________ _______ ________ __________.
________ ______ __________ _________ __________ ______ __________ _____ _____.
____ ________ __________ _______ ______ ________ ___ ________ _________ ________.
______ _________ ______ ______ _________ ______ _____ _______ _________.
________ __________ ______ _______ _________ _________.
____ _____ ____ ______ ___.
_________ _________ ___ __________ ________ __________.
_____ _________ __________ _________ _____ ______.
_________ ____ ________ ________ ___ __________ ______ ____ ______ ___ ___ _______.
____ ___ ___ _____ ___ _______ _________ _____.
______ __________ ______ ______ _________ ______ _______ _____.
_________ _____ ______ __________ _______ _________ ______ __________ _________ _______.
_________ ____ ______ _____ _______.
_______ ___ _______ _____ _________ ___ __________ __________ _______.
____ ___ _______ ______ ____ ___ __________ _______ _________ ________ _______ ___.
_______ ___ __________ _____ ___ ____ ____ _____ _____ _____ _______ ________.
__________ ______ ____ _________ __________.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10