Question

help ?
find the focus and directrix (x-2)^2=-20(y+4)
a) (-7,-4) x=3
b)(2,-9) y=1
c)(3,-4)x=-7
d)(2,1) y=-9

Answer 1

hint:
we can rewrite the equation of your parabola as follows:
\[\Large y + 4 = - \frac{1}{{20}}{\left( {x - 2} \right)^2}\]
now, if we make this traslation:
\[\Large \left\{ \begin{gathered}
y + 4 = Y \hfill \\
x - 2 = X \hfill \\
\end{gathered} \right.\]
where X, Y is the new reference system, we got:
\[\Large Y = - \frac{1}{{20}}{X^2}\]

Answer 2

so would it be b ?

Answer 3

the focus of my parabola is located at:
\[\Large X = 0,Y = - 5\]

Answer 4

now if I substitute those values, I get:
\[\Large \left\{ \begin{gathered}
y + 4 = - 5 \hfill \\
x - 2 = 0 \hfill \\
\end{gathered} \right.\]
please solve for x, and y

Answer 5

y=-9 x=2

Answer 6

correct!

Answer 7

thank you !

Answer 8

the directrix is:
Y=5
so we have:
\[y + 4 = 5\]