Janu16
  • Janu16
What is the equation of the quadratic graph with a focus of (4, 3) and a directix of y = 13?
Mathematics
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SOLVED
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chestercat
  • chestercat
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Janu16
  • Janu16
@AlexandervonHumboldt2
AlexandervonHumboldt2
  • AlexandervonHumboldt2
as the focus is below the directrix then the graph is concave down. line of symmetry is x=4. |dw:1443884034227:dw| distance between the focus and directrix is 2 multiplied by the focal length. distance is 2b = -10 => focal length is b = -5 units vertex is (4. 3 - (-5)) => (4. 8) (x^2−h)=4a(y−k) (x−4^)2=4*(−5)(y−8) now simplify all this and get your equation
AlexandervonHumboldt2
  • AlexandervonHumboldt2
woops mistake wait

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AlexandervonHumboldt2
  • AlexandervonHumboldt2
this is correct distance between the focus and directrix is 2 multiplied by the focal length. distance is 2b = -10 => focal length is b = -5 units vertex is (4. 3 - (-5)) => (4. 8) (x^2−h)=4b(y−k) (x−4)^2=4*(−5)(y−8) now simplify all this and get your equation
Janu16
  • Janu16
so do you simplify both of it?
AlexandervonHumboldt2
  • AlexandervonHumboldt2
not both you simplify this equation (x−4)^2=4*(−5)(y−8)
Janu16
  • Janu16
= −one twentieth (x − 4)2 + 8
Janu16
  • Janu16
|dw:1443884741339:dw|?
Janu16
  • Janu16
@AlexandervonHumboldt2
AlexandervonHumboldt2
  • AlexandervonHumboldt2
yes i think so
AlexandervonHumboldt2
  • AlexandervonHumboldt2
though i could have made a mistake
Janu16
  • Janu16
ok these are thhe my options hold on
Janu16
  • Janu16
|dw:1443885150607:dw|
AlexandervonHumboldt2
  • AlexandervonHumboldt2
the second one as you see
Janu16
  • Janu16
other two options are same as these two but without - 20
AlexandervonHumboldt2
  • AlexandervonHumboldt2
ok
AlexandervonHumboldt2
  • AlexandervonHumboldt2
\(\Huge\color{green}{☺☻}\)
Janu16
  • Janu16
Alright thx for the help and do you think you can help with another similar problem plz?
AlexandervonHumboldt2
  • AlexandervonHumboldt2
i will try but i'm not sure i will do it

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