help on analytic geometry

• Dec 1st 2006, 08:22 AM
help on analytic geometry
Help!!! Just this 1 problem

find the equations of two lines through A, one parallel and the other perpendicular to the line defined by the given equation:
30.) $A(-4,0), 4x+3y = 2$
thats all for today

thank you very much for all your helps!
• Dec 1st 2006, 09:42 AM
CaptainBlack
Quote:

Help!!! Just this 1 problem

find the equations of two lines through A, one parallel and the other perpendicular to the line defined by the given equation:
30.) $A(-4,0), 4x+3y = 2$
thats all for today

thank you very much for all your helps!

Rewrite $4x+3y = 2$ in standard form: $y=-(4/3)x+2/3$ so the slope of lines parallel to this all have slope $-4/3$, and the slope of a line perpendicular to this has slope $3/4$.

Now the equation of the parallel line is:

$
y=-(4/3)x+c
$

now it goes through $(-4,0)$, so $0=-(4/3)(-4)+c$
so $c=-16/3$, so:

$
y=-(4/3)x-16/3
$
.

A similar procedure gives the line at right angle to this one as:

$
y=(3/4)x+3
$

RonL