Fin the differential equations of the following Solve the following problems.1-y1) A curve in a rectangular coordinates is to have a slope equal.to-Findits equation if it passes through (1,4).2) Find the equation of the curve if every point on it the tangent line has aslope equal tox+y3) A curve in rectangular coordinates is drawn so that every point on it isequidistant from the origin and the intersection of the y-axis with the normalto the curve at that point. Find its equation.4) Find the equation of the curve whose segment of each tangent between thecoordinate axes is bisected by the point of tangency.5) Find the orthogonal trajectories of the family of cubics x? = Cy°. Find alsothe 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 atthe origin and foci on the x-axis.8) Find the isogonal trajectories intersecting at 45° to the family of hyperbolasy(x-C) = 1.9) Find the isogonal trajectories cutting at an angle of arctan 4 to the familywhose equation is y = Inx+ C.10) Find the isogonal trajectories cutting at an angle of 45° to the family of linespassing through the origin.

As there are a lot of questions and nothing is mentioned which question to to , So I will solve only…

Answered: A curve in a rectangular coordinates is…

Math

Advanced Math

A curve in a rectangular coordinates is to have a slope equal.to - Find its equation if it passes through (1, 4).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Fin the differential equations of the following

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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