equation of a line

jayjay60 · #1 $Old$ September 27th, 2009, 01:30 PM

Find an equation of the line that is both normal to the given parabola and also parallel to the given line

Find an equation of the line that is both normal to the given parabola and also parallel to the given line.
y = 5 x^2 - 5 x + 6
x - 5 y = 6

[color=black]i'm trying to figure out graphs all day.
care to explain this?
i'll give you a hug?

skeeter · #2 $Old$ September 27th, 2009, 02:14 PM

Quote:

Originally Posted by jayjay60 $View Post$

Find an equation of the line that is both normal to the given parabola and also parallel to the given line

Find an equation of the line that is both normal to the given parabola and also parallel to the given line.
y = 5 x^2 - 5 x + 6
x - 5 y = 6

line's slope is $m = \frac{1}{5}$

the normal line to the parabola will also have this slope.

look for the line tangent to the parabola with slope $m = -5$

$y' = 10x - 5 = -5$

$x = 0$ , $y(0) = 6$ ... point on the parabola is $(0,6)$

line normal to the parabola that is parallel to the given line will be

$y - 6 = \frac{1}{5}(x - 0)$

jayjay60 · #3 $Old$ September 27th, 2009, 02:28 PM

thank you so much!