In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. ANS. (y ANS. y dx - x dy = 0. 3. Straight lines with slope and y-intercept equal. 4. Straight lines with slope and x-intercept equal. 5. Straight lines with algebraic sum of the intercepts fixed as k. ANS. 7. Circles with center at the origin. 8. Circles with center on the x-axis. 9. Circles with fixed radius r and tangent to the x-axis. 10. Circles tangent to the x-axis. - k) dx − (x − h) dy = 0. y dx - (x + 1) dy = 0. ANS. (y)² = xy' — y. ANS. (xy' — y)(y' − 1) + ky' = 0. - 6. Straight lines at a fixed distance p from the origin. ANS. (xy' - y)² = p²[1 + (y′)²]. ANS. x dx + y dy = 0. ANS. yy" + (y)² + 1 = 0. ANS. (y ± r)²(y')² + y² ± 2ry = 0. ANS. [1 + (y')²]³ = [yy″ + 1 + (y')²]².
In each exercise, obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Straight lines through the origin. 2. Straight lines through the fixed point (h, k); h and k not to be eliminated. ANS. (y ANS. y dx - x dy = 0. 3. Straight lines with slope and y-intercept equal. 4. Straight lines with slope and x-intercept equal. 5. Straight lines with algebraic sum of the intercepts fixed as k. ANS. 7. Circles with center at the origin. 8. Circles with center on the x-axis. 9. Circles with fixed radius r and tangent to the x-axis. 10. Circles tangent to the x-axis. - k) dx − (x − h) dy = 0. y dx - (x + 1) dy = 0. ANS. (y)² = xy' — y. ANS. (xy' — y)(y' − 1) + ky' = 0. - 6. Straight lines at a fixed distance p from the origin. ANS. (xy' - y)² = p²[1 + (y′)²]. ANS. x dx + y dy = 0. ANS. yy" + (y)² + 1 = 0. ANS. (y ± r)²(y')² + y² ± 2ry = 0. ANS. [1 + (y')²]³ = [yy″ + 1 + (y')²]².
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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JUST SKETCH THE GRAPHS PLEASE. NOS. 1-10
![In each exercise, obtain the differential equation of the family of plane curves described
and sketch several representative members of the family.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
ANS. y dx x dy = 0.
ANS. (y — k) dx − (x − h) dy = 0.
-
ANS.
y dx
(x + 1) dy = 0.
(y)² = xy' — y.
3. Straight lines with slope and y-intercept equal.
4. Straight lines with slope and x-intercept equal.
5. Straight lines with algebraic sum of the intercepts fixed as k.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
ANS. (xy' — y)(y' − 1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
ANS.
9. Circles with fixed radius r and tangent to the x-axis.
ANS.
10. Circles tangent to the x-axis.
ANS.
(xy' — y)² = p²[1 + (y')²].
ANS. x dx + y dy = 0.
ANS. yy" + (y')² + 1
=
: 0.
(y ± r)²(y')² + y² ± 2ry = 0.
ANS. [1 + (y')²]³ = [yy” + 1 + (y')²]².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8943d76e-c254-4322-8f39-c91cdf9301f3%2F5caa57d3-185b-4e58-9e73-9a79cdabce5c%2F1emx1qj_processed.png&w=3840&q=75)
Transcribed Image Text:In each exercise, obtain the differential equation of the family of plane curves described
and sketch several representative members of the family.
1. Straight lines through the origin.
2. Straight lines through the fixed point (h, k); h and k not to be eliminated.
ANS. y dx x dy = 0.
ANS. (y — k) dx − (x − h) dy = 0.
-
ANS.
y dx
(x + 1) dy = 0.
(y)² = xy' — y.
3. Straight lines with slope and y-intercept equal.
4. Straight lines with slope and x-intercept equal.
5. Straight lines with algebraic sum of the intercepts fixed as k.
7. Circles with center at the origin.
8. Circles with center on the x-axis.
ANS. (xy' — y)(y' − 1) + ky' = 0.
6. Straight lines at a fixed distance p from the origin.
ANS.
9. Circles with fixed radius r and tangent to the x-axis.
ANS.
10. Circles tangent to the x-axis.
ANS.
(xy' — y)² = p²[1 + (y')²].
ANS. x dx + y dy = 0.
ANS. yy" + (y')² + 1
=
: 0.
(y ± r)²(y')² + y² ± 2ry = 0.
ANS. [1 + (y')²]³ = [yy” + 1 + (y')²]².
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