Question

What is the general equation of tangent of parabola?

Answer 1

Here we list the equation of tangent and normal for different forms of parabola:

Equation of tangent to the parabola y2=4axy2=4ax at (x1,y1)(x1,y1) is
yy1=2a(x+x1)yy1=2a(x+x1)

Equation of normal to the parabola y2=4axy2=4ax at (x1,y1)(x1,y1) is
y−y1=−y12a(x+x1)y−y1=−y12a(x+x1)

If −y12a=m−y12a=m then equation of normal line is
y=mx−2am−am3

The line y=mx+cy=mx+c touches the parabola
y2=4axy2=4ax
if c=amc=am

Equation of tangent to the parabola y2=4axy2=4ax at (at2,2at)(at2,2at) is
x−ty+at2=0x−ty+at2=0

Equation of normal to the parabola y2=4axy2=4ax at (at2,2at)(at2,2at) is
y+tx=2at+at3