anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Michele_Laino
  • 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: \[\Large Y = - \frac{1}{{20}}{X^2}\]
anonymous
  • anonymous
so would it be b ?
Michele_Laino
  • Michele_Laino
the focus of my parabola is located at: \[\Large X = 0,Y = - 5\]

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Michele_Laino
  • 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
anonymous
  • anonymous
y=-9 x=2
Michele_Laino
  • Michele_Laino
correct!
anonymous
  • anonymous
thank you !
Michele_Laino
  • Michele_Laino
the directrix is: Y=5 so we have: \[y + 4 = 5\]

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