What is the reciprocal of -7/9?

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Ответ:

jahootey2798

15.04.2023

Mathematics

$\displaystyle y=\frac{1}{4}x^2$

Step-by-step explanation:

Let (x, y) be a point on the parabola.

By definition, any point on the parabola is equidistant from the focus and the directrix

The distance from the focus is given by:

$\begin{aligned} d&=\sqrt{(x-0)^2+(y-1)^2\\\\&=\sqrt{x^2+(y-1)^2}\end{aligned}$

The distance from the directrix is given by:

$d=|y-(-1)|=|y+1|\text{ or } |-1-y|$

So:

$\sqrt{x^2+(y-1)^2}=|y+1|^$

Square both sides. Since anything squared is positive, we can remove the absolute value:

x^2+(y-1)^2=(y+1)^2

Square:

x^2+(y^2-2y+1)=y^2+2y+1

Hence:

x^2=4y

So, our equation is:

$\displaystyle y=\frac{1}{4}x^2$

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