## anonymous one year ago 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

1. Michele_Laino

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: $\Large Y = - \frac{1}{{20}}{X^2}$

2. anonymous

so would it be b ?

3. Michele_Laino

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

4. Michele_Laino

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

5. anonymous

y=-9 x=2

6. Michele_Laino

correct!

7. anonymous

thank you !

8. Michele_Laino

the directrix is: Y=5 so we have: $y + 4 = 5$