A curve in a rectangular coordinates is to have a slope equal.to - Find its equation if it passes through (1, 4).
A curve in a rectangular coordinates is to have a slope equal.to - Find its equation if it passes through (1, 4).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Solve the following problems.
1-y
1) A curve in a rectangular coordinates is to have a slope equal.to-
Find
its equation if it passes through (1,4).
2) Find the equation of the curve if every point on it the tangent line has a
slope equal to
x+y
3) A curve in rectangular coordinates is drawn so that every point on it is
equidistant from the origin and the intersection of the y-axis with the normal
to the curve at that point. Find its equation.
4) Find the equation of the curve whose segment of each tangent between the
coordinate axes is bisected by the point of tangency.
5) Find the orthogonal trajectories of the family of cubics x? = Cy°. Find also
the particular trajectory which passes through (1, 4).
6) Find the orthogonal trajectories of the family of circles with centers at the
- origin.
7) Find the orthogonal trajectories of the family of parabolas with vertices at
the origin and foci on the x-axis.
8) Find the isogonal trajectories intersecting at 45° to the family of hyperbolas
y(x-C) = 1.
9) Find the isogonal trajectories cutting at an angle of arctan 4 to the family
whose equation is y = Inx+ C.
10) Find the isogonal trajectories cutting at an angle of 45° to the family of lines
passing through the origin.
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