Respuesta :

TheSandman1337
Suppose that the point A(x,y) belongs to this parabola. The defining point of the parabola is that the distance between a point F and the directrix. Suppose that the chosen point F is at (a,b). Then, the distance from A to the directrix is |b+4| while the distance from A to the focus is given by the pythagorean theorem:
[tex]d= \sqrt{(x-a)^2+(y-b)^2} [/tex].
We have that these two have to be equal. Squaring both sides we get:
[tex]b^2+8b+16=(x-a)^2+(y-b)^2[/tex].
This is the equation that describes all equations of parabolas with that directrix; you just need to choose the focus and substituting a and b will yield the equation.
nightmaremangle68

Answer:

The correct answers are as follows:

[tex]x=\frac{y^{2} }{24} -\frac{7y}{12} +\frac{97}{24}[/tex]

[tex]x=-\frac{y^{2} }{16} +\frac{5y}{8} -\frac{153}{16}[/tex]

[tex]x=\frac{y^{2} }{32}+ \frac{3y}{16} +\frac{137}{32}[/tex]

These all have a directrix of -4, while the others have -2, -3, and -6.

You are welcome.

~Kicho [nm68]

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