Parabola

[BigGlenntheHeavy]

Find an equation of the following parabola.

Directrix y = 1, length of latus rectum = 8, opens downward.

 

[Denis]

Get some practice/refresher here:
http://www.mathhelpforum.com/math-help/ ... ctrix.html

 

[soroban]

Hello, BigGlenntheHeavy!

There is insufficient information for a unique solution.

Find an equation of the following parabola:
. . Directrix: \(\displaystyle y = 1\), length of latus rectum = 8, opens downward.

\(\displaystyle \text{Since the parabola opens downward,}\)

\(\displaystyle \text{the general form is: }\x-h)^2 \:=\:-4p(y-k)\)

. . \(\displaystyle \text{where }(h,k)\text{ is the Vertex, and }p\text{ is the distance from the Vertex to the Focus}\)
. . \(\displaystyle and\text{ the distance from the Vertex to the Directrix.}\)


\(\displaystyle \text{Fact: the length of the Latus Rectum is }4p.\)

. . \(\displaystyle \text{Hence: }\:4p \,=\,8 \quad\Rightarrow\quad p \,=\,2\)


So far, we have:

      |
    . + . . . . . . . y = 1
      |
      |
  ----+----------------------
      |
      |     (h,-1)
      |       o
      |   *       *
      | *           *
      |*             *
      |
      *               *
      |

\(\displaystyle \text{The directrix is: }\,y = 1\)

\(\displaystyle \text{We have: }\ = 2.\)

\(\displaystyle \text{The vertex is: }\h,-1)\)

\(\displaystyle \text{The equation is: }\x-h)^2 \:=\:-8(y+1)\)

 

[BigGlenntheHeavy]

Right on Soroban, you are indeed a mathematicican