The equation xdy + ydx-O represents a family of Acurve is called an isegenal trajectely er antr Gieen (zy + v) dr + (r -v) dy - 0, nterct ony o er f the fenly a O hyperbolas O 1-2xy iterecttst onmee ofhe f O parabolas 1+ 2xy tersects eery menber of the fyata O straight lines -2xy-1 rct er themeber O drcdes O 1+ 2xy The orthogonal trajectories of the family of curves y ax' i The solution curves of the given ditferential equation: dx- dy O constitute a fay of O parabolas O dircles hyperbolas O straight lines

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Online Activity - Mastery test (part2) DIFEQU. Please answer all 5 questions. Thanks! 

The equation xdy + ydx = 0 represents a family of
A curve is called an isogonal trajectoiy or an x trajectory of family f(x, y, c) = 0 if
ƏM
Given (xy + y) da + (x – a'y) dy = 0,
-
dy
It intersects only one member of the family at an angle a
hyperbolas
1- 2xy
It intersects at least one member of the family at an angle a.
parabolas
1 + 2xy
It intersects every member of the family at an angle a
straight lines
-2xy -1
It intersects either none of the members of the family or every member of the family at an angle a
circles
-1 + 2xy
The orthogonal trajectories of the family of curves y = ax? is
The solution curves of the given differential equation: xdx - dy = 0 constitute a famly of
x² – 2y? = c2
parabolas
o y? – 2x? = c²
circles
hyperbolas
x² + 2y? = c?
straight lines
y? + 2x? = c?
Transcribed Image Text:The equation xdy + ydx = 0 represents a family of A curve is called an isogonal trajectoiy or an x trajectory of family f(x, y, c) = 0 if ƏM Given (xy + y) da + (x – a'y) dy = 0, - dy It intersects only one member of the family at an angle a hyperbolas 1- 2xy It intersects at least one member of the family at an angle a. parabolas 1 + 2xy It intersects every member of the family at an angle a straight lines -2xy -1 It intersects either none of the members of the family or every member of the family at an angle a circles -1 + 2xy The orthogonal trajectories of the family of curves y = ax? is The solution curves of the given differential equation: xdx - dy = 0 constitute a famly of x² – 2y? = c2 parabolas o y? – 2x? = c² circles hyperbolas x² + 2y? = c? straight lines y? + 2x? = c?
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