anonymous
  • anonymous
Find the vertex, focus, directrix, and focal width of the parabola. x = 4y^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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perl
  • perl
The general form of your parabola is $$ \Large x = \frac {1}{4p} y^2 $$Focal width is 4p
anonymous
  • anonymous
ok what do i do wuth that formula
perl
  • perl
we need to solve 1/(4p) = 4

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anonymous
  • anonymous
oh so p = 1/16?
perl
  • perl
yes
perl
  • perl
the vertex is (h,k) directrix is x = -p focal width is 4p
perl
  • perl
it is centered at the origin
anonymous
  • anonymous
how do we find h and k
anonymous
  • anonymous
ok the focal width is .25
perl
  • perl
The general form of a parabola that opens to the right or left \[ \Large x-h = \frac {1}{4p} (y-k)^2 \]Vertex is (h,k) directrix is x =h -p focal width is 4p
perl
  • perl
yes that is correct
anonymous
  • anonymous
is the focal width represented as a single letter?
perl
  • perl
4 times that value of p
anonymous
  • anonymous
like i know i can plug in x as 4y^2 but thats still not enough to find either h or k
perl
  • perl
h must be zero and k must be zero
anonymous
  • anonymous
how do you know its at the origin though
anonymous
  • anonymous
oh wait all the choices have the vertix set to (0,0) but if it isnt how do you know
perl
  • perl
\[ \Large x-h = \frac {1}{4p} (y-k)^2 \iff x = \frac {1}{4p} y^2 \]
perl
  • perl
the two equation left sides must match and the right side must match
anonymous
  • anonymous
ohhhhhh omg ok i get it
perl
  • perl
the two equations left sides must match and right sides
anonymous
  • anonymous
and thats how you know its at the origin?
perl
  • perl
yes. or by graphing it
anonymous
  • anonymous
ok then the directrix is 0-.25 which would = -1/4
anonymous
  • anonymous
but what about the focus?
perl
  • perl
correct. and the focus is (h+ p, k )
anonymous
  • anonymous
oh ok this is actually simplier than i thought! thank you so much!

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