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Obtain the differential equation of the family of all parabolas whose vertices are at the origin and whose axes are horizontal. A. 2xy'-y=0 B. xy'-2y=0 C. 2y'+xy=0 D. 2x+чy'=0 Find the equation of the curve at every point of which the tangent line has a slope of x² and which passes through (1, 1). A. x3 + 3y-2=0 B. x3+3y²+2=0 C. x³- 3y + 2 =0 D. x3 - 2 + 3 = 0 Find the orthogonal trajectories of the family of curves x=ky2, where k is an arbitrary constant. A. 2x² + y² = C B. x²+2y² = C C. 2x²- y² = C D. x²-2y² = C

Obtain the differential equation of the family of all parabolas whose vertices are at the origin and whose axes are horizontal. A. 2xy'-y=0 B. xy'-2y=0 C. 2y'+xy=0 D. 2x+чy'=0 Find the equation of the curve at every point of which the tangent line has a slope of x² and which passes through (1, 1). A. x3 + 3y-2=0 B. x3+3y²+2=0 C. x³- 3y + 2 =0 D. x3 - 2 + 3 = 0 Find the orthogonal trajectories of the family of curves x=ky2, where k is an arbitrary constant. A. 2x² + y² = C B. x²+2y² = C C. 2x²- y² = C D. x²-2y² = C

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Obtain the differential equation of the family of all parabolas whose vertices are at the origin and whose axes are horizontal. A. 2xy'-y=0 B. xy'-2y=0 C. 2y'+xy=0 D. 2x+чy'=0 Find the equation of the curve at every point of which the tangent line has a slope of x² and which passes through (1, 1). A. x3 + 3y-2=0 B. x3+3y²+2=0 C. x³- 3y + 2 =0 D. x3 - 2 + 3 = 0 Find the orthogonal trajectories of the family of curves x=ky2, where k is an arbitrary constant. A. 2x² + y² = C B. x²+2y² = C C. 2x²- y² = C D. x²-2y² = C
Transcribed Image Text:Obtain the differential equation of the family of all parabolas whose vertices are at the origin and whose axes are horizontal. A. 2xy'-y=0 B. xy'-2y=0 C. 2y'+xy=0 D. 2x+чy'=0 Find the equation of the curve at every point of which the tangent line has a slope of x² and which passes through (1, 1). A. x3 + 3y-2=0 B. x3+3y²+2=0 C. x³- 3y + 2 =0 D. x3 - 2 + 3 = 0 Find the orthogonal trajectories of the family of curves x=ky2, where k is an arbitrary constant. A. 2x² + y² = C B. x²+2y² = C C. 2x²- y² = C D. x²-2y² = C
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