Question

directrix =-2 and focus is at (4,3) find equation and the vertex

Answer 1

@freckles

Answer 2

x=-2?

Answer 3

vertex = -2

Answer 4

-2? so..hmmm shouldn't it be an ordered pair? 0,-2? -2,0?

Answer 5

actually i think the directrix is -2

Answer 6

well then, you found it already then =)

Answer 7

i need help finding the eq and vertex

Answer 8

well, the directrix should have an equation
x = -2? y = -2?

Answer 9

x = -2

Answer 10

so.. where do you think the vertex would be?

Answer 11

1,3

Answer 12

how do i find equation

Answer 13

well, right.. 1,3 is correct.. the equation is ahemm

notice the distance from the vertex to either, the focus or directrix, is 3 units
thus p = 3
and it's also a horizontal parabola
thus
\(\bf \begin{array}{llll}
(y-{\color{blue}{ k}})^2=4{\color{purple}{ p}}(x-{\color{brown}{ h}}) \\
(x-{\color{brown}{ h}})^2=4{\color{purple}{ p}}(y-{\color{blue}{ k}})\\
\end{array}

\qquad
\begin{array}{llll}
vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\
{\color{purple}{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\qquad thus
\\ \quad \\
\begin{array}{llll}
(y-{\color{blue}{ 3}})^2=4{\color{purple}{ (3)}}(x-{\color{brown}{ 1}}) \\

\end{array}

\qquad
\begin{array}{llll}
vertex\ ({\color{brown}{ 1}},{\color{blue}{ 3}})\\
{\color{purple}{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\)

Answer 14

because is a horizontal parabola, the "y" is the squared variable

Answer 15

would... but need to dash in 1 sec :|

Answer 16

okay