TymariY647418 TymariY647418
  • 03-11-2022
  • Mathematics
contestada

a) which is equation of the parabola? b) name the focus and directrix ? c) name vertex and axis of symmetry?

Respuesta :

NikitaM180543 NikitaM180543
  • 03-11-2022

The equation of the parabola whose axis of symmetry is parallel to x-axis is

[tex](y-k)^2=4p(x-h)[/tex]

where the focus is

[tex]\text{focus}=(h+p,k)[/tex]

and the directrix is

[tex]x=h-p[/tex]

In our case, the focus is (6,1) and the directrix is x =2; therefore, we have

[tex](6,1)=(h+p,k)[/tex]

and

[tex]h-p=2[/tex]

These equations give

[tex]k=1,h=4,p=2[/tex]

Hence, the equation of the parabola is

[tex](y-1)^2=8(x-4)[/tex]

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