what is the equation of a parabola with vertex (0,0) and focus (0,-1.5)

how do i find that equation

what are the vertex, focus, and directrix of a parabola with equation \(y=\frac{x^2}{4}\)

how do i find them

what is a focus

what is a directrix

how does the distance of the focus from the vertex affect the shape of a parabola

why

and dude wheres my car

OfficialBubbleTanks
Mar 9, 2018

#1**+1 **

4py = x^2 p = -1.5 ....so....

4 (-1.5)y = x^2

-6y = x^2

y = (-1/6)x^2

y = x^2 / 4

4y = x^2 the vertex is (0,0)

To find the focal length, we have

4p = 4 ⇒ p = 1

So....the focus is (0, 0+ p) = (0 , 1)

The directrix is y = -1

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix.

The longer the focus, the wider the parabola.....

CPhill
Mar 9, 2018