Parabola is curve graph such that each ordered pair `(x,y)` is equidistant distance to the fixed line (directrix) and fixed point (foci). We have "p" units as distance of foci or directrix from the vertex. A parabola with vertex at the origin `(0,0)` follow standard formula as:
a) `x^2 =4py` when parabola opens upward
b) `x^2 =-4py ` when parabola opens downward
c) `y^2 =4px` when parabola opens to the right
d) `y^2...
Parabola is curve graph such that each ordered pair `(x,y)` is equidistant distance to the fixed line (directrix) and fixed point (foci). We have "p" units as distance of foci or directrix from the vertex. A parabola with vertex at the origin `(0,0)` follow standard formula as:
a) `x^2 =4py` when parabola opens upward
b) `x^2 =-4py ` when parabola opens downward
c) `y^2 =4px` when parabola opens to the right
d) `y^2 =-4px` when parabola opens left.
The given equation `y^2=16x ` resembles the standard formula `y^2=4px` .
Thus, the parabola opens to the right and we may solve for p using:
`4p =16`
`(4p)/4 = 16/4`
`p =4`
When parabola opens sideways, that means the foci and vertex will have the same values of `x` . We follow the properties of the parabola that opens to right as:
vertex at point `(h,k)`
foci at point `(p,k)`
directrix at` x= k-p`
axis of symmetry: `y =k`
endpoints of latus rectum: `(p,2p)` and` (p, -2p)`
Using vertex `(0,0)` , we have `h =0` and` k=0` .
Applying `k=0` and `p=4` , we get the following properties:
a) foci at point `( 4, 0)`
b) axis of symmetry: `y=0` .
c) directrix at `x= 0-4 or x=-4.`
d) Endpoints of latus rectum: `(4,2*4)` and `(4, -2*4)` simplify to `(4,8)` and `(4.-8)` .
To graph the parabola, we connect the vertex with the endpoints of the latus rectum and extend it at both ends. Please see the attached file for the graph of `y^2=16x.`
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