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What is the equation of the parabola, in vertex form, with focus at (1,-4) and
directrix x= 3?

What Is The Equation Of The Parabola In Vertex Form With Focus At 14 And Directrix X 3 class=

Sagot :

evgeniylevi

Answer:

D.

Step-by-step explanation:

1) according to the definition of parabola d(focus)=f(directrix),

2) then

[tex]d(focus)=\sqrt{(x-1)^2+(y+4)^2} \ and \ d(directrix)=|x-3|;[/tex]

[tex]\sqrt{(x-1)^2+(y+4)^2} =|x-3|;[/tex]

3) after evoluation the equation:

(y+4)²=-4x+8 or (y+4)²= -4(x-2);

4) correct answer is D.

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