parabola 4 types concept standard form

Parabola 4 types concept in standard form:

parabola 4 types        →	1	2	3	4
Equation of Parabola                                                 →	y²= 4ax    ↓	y²=-   4ax          ↓	x²=  4ay      ↓	x²=  –   4ay    ↓
Directrix of Parabola	x  = – a	x  =  a	y  =  -a	y  =  a
Focus of parabola  →	(a, 0)	(-a, 0)	(0, a)	(0,  -a)
Vertex of parabola →	(o, o)	(o, o)	(o, o)	(o, o)
Axis of Parabola  →	y   =  0	y  =   0	x   =   0	x   =   0
Latusrectum of parabola	x  =  a	x   =   -a	y   =a	y  =  -a

parabola 4 types concept standard form:

Graph of parabola Type 1:

y²= 4ax

Graph of parabola Type 2 in standard form

y²=    –   4ax

Graph of parabola Type 3 in standard form:

Graph of parabola Type 4 in standard form:

Analyze the parabola example

analyze the parabola x² = – 16y

SOLUTION:

we compare the given equation

with     x²= – 4 a y

here,

4a = 16 

  or

  a = 4

the focus of the parabola lies on the y-axis, and its opening is downward.

Coordinate of the focus = (0, -4)

equation of axis is x =0

Length of the latusrectum is 16 and y= 0 is tangent to the parabola at its vertex.