# Thread: [SOLVED] Normal line to a curve

1. ## [SOLVED] Normal line to a curve

The original equation is y=sqrtx/(x+4)
and the question asks to find the equation of tangent and normal line at point (9,3/13)

so I derived and found the tangent line to be y=-5/1020x + 243/884 and that is the correct answer, but I keep getting the normal line wrong

So for the normal line's slope I went -1/m and I got so the slope 1020/5 which is 204. and then I plugged it in to y-3/13=204(x-9)

and that gives y=204x-23865/13

I've redone it over and over again, but it still says the answer is wrong.

I'm just wondering where I went wrong.
Thank you for helping me!!!

2. Originally Posted by electricsparks
The original equation is y=sqrtx/(x+4)
and the question asks to find the equation of tangent and normal line at point (9,3/13)

so I derived and found the tangent line to be y=-5/1020x + 243/884 and that is the correct answer, but I keep getting the normal line wrong

So for the normal line's slope I went -1/m and I got so the slope 1020/5 which is 204. and then I plugged it in to y-3/13=204(x-9)

and that gives y=204x-23865/13

$\color{red}\mbox{I get here in the fraction }\,\frac{23868}{13}=1836$

Tonio

I've redone it over and over again, but it still says the answer is wrong.

I'm just wondering where I went wrong.
Thank you for helping me!!!
.

3. Originally Posted by electricsparks
The original equation is y=sqrtx/(x+4)
and the question asks to find the equation of tangent and normal line at point (9,3/13)

so I derived and found the tangent line to be y=-5/1020x + 243/884 and that is the correct answer, but I keep getting the normal line wrong

That isn't the correct equation for the tangent. Differentiating and plugging in x=9 gives the tangent slope as $\frac{-5}{1014}$ which gives the tangent as: $y = \frac{-5x}{1014} + \frac {93}{338}$

So for the normal line's slope I went -1/m and I got so the slope 1020/5 which is 204. and then I plugged it in to y-3/13=204(x-9)

So the slope of the normal is now $\frac{1014}{5}$. I think you can work it out from there.

and that gives y=204x-23865/13

I've redone it over and over again, but it still says the answer is wrong.

I'm just wondering where I went wrong.
Thank you for helping me!!!
..

4. Oh! ok, I see where I went wrong. That was a dumb mistake. Thanks!