Normal Line to a Tangent

Key Questions

How do you find the equation of a normal line if you know the equation of the tangent line?

If a tangent line has the equation

$y-y_1=m(x-x_1)$ ,

then the normal line at the point of contact is

$y-y_1=-1/m(x-x_1)$ .

I hope that this was helpful.

Wataru · · Oct 19 2014
If my tangent line at point (4,8) has the equation $y=5x/6 - 9$ , what is the equation of the normal line at the same point?

The normal line is the line that is perpendicular to the the tangent line.

If the slope of a line is $m$ then the slope of the perpendicular line is $-1/m$ , this is also known as the negative reciprocal.

The given equation is $y=5/6x-9$ the slope is $5/6$ so the slope of the normal is $-6/5$ .

The point $(x,y)->(4,8)$

$y=mx+b ->$ Substitute in the values of $m$ , $x$ and $y$

$8=-6/5(4)+b$

$8=-24/5+b$

$24/5+8=b$

$24/5+40/5=b$

$64/5=b$

The equation of the normal line is $-> y=-6/5x+64/5$

AJ Speller · · Oct 11 2014
What is a Normal Line to a Tangent?

A normal line is the line perpendicular to a tangent line at the point of contact.

Wataru · · Sep 11 2014