Active forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling
New forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft
Recent comments
- 400000=120[14π(D2−10000)]
(…1 month ago - Use integration by parts for…1 month 4 weeks ago
- need answer1 month 4 weeks ago
- Yes you are absolutely right…2 months ago
- I think what is ask is the…2 months ago
- $\cos \theta = \dfrac{2}{…2 months ago
- Why did you use (1/SQ root 5…2 months ago
- How did you get the 300 000pi2 months ago
- It is not necessary to…2 months ago
- Draw a horizontal time line…2 months 1 week ago
Since the vertex and focus
Since the vertex and focus are on the $x-axis$, then their coordinates are in the form $(a,0)$ and $(b,0)$ respectively. The general equation of a parabola with axis of symmetry at the $x-axis$ is $(x-a)^2 = 4ky$. There will be two arbitrary constants since there is no fixed vertex/focus and length of latus rectum.
$$\begin{eqnarray}
(x-a)^2 &=& 4ky\\
(x-a)^2 y^(-1) &=& 4k\\
2(x-a)y^(-1) - (x-a)^2 y^(-2)y'&=& 0\\
2y - (x-a)y' &=& 0\\
x - \dfrac{2y}{y'} &=& a\\
1 - \dfrac{2y' y' - 2yy''}{(y')^2} &=& 0\\
(y')^2 - (2(y')^2 - 2yy'') &=& 0\\
-(y')^2 + 2yy'' &=& 0\\
(y')^2 - 2yy'' &=& 0 \rightarrow Answer
\end{eqnarray}$$