# Thread: help on analytic geometry

1. ## 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.) $\displaystyle A(-4,0), 4x+3y = 2$
thats all for today

thank you very much for all your helps!

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.) $\displaystyle A(-4,0), 4x+3y = 2$
thats all for today

thank you very much for all your helps!
Rewrite $\displaystyle 4x+3y = 2$ in standard form: $\displaystyle y=-(4/3)x+2/3$ so the slope of lines parallel to this all have slope $\displaystyle -4/3$, and the slope of a line perpendicular to this has slope $\displaystyle 3/4$.

Now the equation of the parallel line is:

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

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

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

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

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

RonL