# What is the focus, vertex, and directrix of the parabola described by #16x^2=y#?

##### 2 Answers

**Vertex is at** **directrix is** **and focus is at**

#### Explanation:

of equation ,

equidistance from focus and directrix situated at opposite sides.

since

vertex is

Focus is at

graph{16x^2 [-10, 10, -5, 5]} [Ans]

#### Explanation:

#"express the equation in standard form"#

#"that is "x^2=4py#

#rArrx^2=1/16y#

#"this is the standard form of a parabola with the y-axis"#

#"as its principal axis and vertex at the origin"#

#"if 4p is positive graph opens up, if 4p is"#

#"negative the graph opens down"#

#rArrcolor(blue)"vertex "=(0,0)#

#"by comparison " 4p=1/16rArrp=1/64#

#"focus "=(0,p)#

#rArrcolor(red)"focus "=(0,1/64)#

#"equation of directrix is " y=-p#

#rArrcolor(red)"equation of directrix " y=-1/64#