MHB Find Equation of Parabola Given Focus & Directrix - Jose's Q&A

  • Thread starter Thread starter MarkFL
  • Start date Start date
  • Tags Tags
    Focus Parabola
MarkFL
Gold Member
MHB
Messages
13,284
Reaction score
12
Here is the question:

Writing an equation given the directrix and focus?


focus: (3,5) directrix y=1. write an equation for the parabola. How do I do this? please help!

I have posted a link there to this thread so the OP can view my work.
 
Mathematics news on Phys.org
Re: jose's question at Yahoo! Questions: find the equation of the parabola given the focus and direc

Hello jose,

Let's let $(x,y)$ be an arbitrary point on the parabola. Now, we know the perpendicular distance from the point to the directrix will be equal to the distance between this point and the focus. Thus, we may state:

$$|y-1|=\sqrt{(x-3)^2+(y-5)^2}$$

Square both sides:

$$(y-1)^2=(x-3)^2+(y-5)^2$$

Expand binomials:

$$y^2-2y+1=x^2-6x+9+y^2-10y+25$$

Collect like terms:

$$8y=x^2-6x+33$$

Divide through by $8$:

$$y=\frac{x^2-6x+33}{8}$$
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Back
Top