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A parabola has a focus at ( 1.5, 0) and a directrix of x= -1.5. Which of the following equations represent the parabola?

C X A Parabola Has A Focus At 15 0 And A Directrix Of X 15 Which Of The Following Equations Represent The Parabola class=

Sagot :

Step-by-step explanation:

Since the focus lies on the x axis, and the diretcrtirx is a vertical line, we have a sideways parabola so we have the equation

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

where h,k is the vertex and

p is the distance from the vertex to the focus or the distance fromcthe vertex to the directrix.

Since the focus is 1.5, and the directrix is -1.5 the vertex is (0,0) so we have

[tex]y {}^{2} = 4px[/tex]

We know p is 1.5 so we have

[tex] {y}^{2} = 6x[/tex]

[tex] \frac{1}{6 } {y}^{2} = x[/tex]

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