"What is the families of the curve of all Parabolas with axis parallel to the x-axis

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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From the question and answer of "What is the families of the curve of all Parabolas with axis parallel to the x-axis" 

Determine the result of elimination of constant.
Where is the answer for "Result of elimination of constant"

Step 1
The equation of a parabola with vertex at (h,k) latus rectum equal
to 4a and axis parallel to X axis is,
(y – k)? = 4a(x – h)
y2 – 2yk + k2 = 4ax – 4ah
Differentiate y,
2у — 2k 3 4а
dy
dx
Differentiate with respect to y,
2 = 4a-
d²x
dy
d'x
dy?
1
2a
Again differentiate with respect to y,
= )
dy3
Transcribed Image Text:Step 1 The equation of a parabola with vertex at (h,k) latus rectum equal to 4a and axis parallel to X axis is, (y – k)? = 4a(x – h) y2 – 2yk + k2 = 4ax – 4ah Differentiate y, 2у — 2k 3 4а dy dx Differentiate with respect to y, 2 = 4a- d²x dy d'x dy? 1 2a Again differentiate with respect to y, = ) dy3
Step 2
Now convert the equation,
dx
dy
dy
dx
d²x
dy?
d
1
dy
dy
dx
4=(+):
d³x
d
1
dx
dy3
dx
dy
dy
dx
d³x
d²y
-1
dy
3
dx2
dx
(台)
dy d³y
3
dz2
-
d³x
dx dx³
4
dy3
dy
dx
dy d'y
3
dx dx3
0 =
4
dy
dx
3()-些=0
2
dy d³y
dx dx3
d'y
dx2
||
Transcribed Image Text:Step 2 Now convert the equation, dx dy dy dx d²x dy? d 1 dy dy dx 4=(+): d³x d 1 dx dy3 dx dy dy dx d³x d²y -1 dy 3 dx2 dx (台) dy d³y 3 dz2 - d³x dx dx³ 4 dy3 dy dx dy d'y 3 dx dx3 0 = 4 dy dx 3()-些=0 2 dy d³y dx dx3 d'y dx2 ||
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