Find the normal line to the curve x^2 + 2y = 8 andperpendicular to the line x -2y + 4 = 0

Question

amistre64 · Answer

you need to determine the derivative

amistre64 · Answer

since a normal is perpendicular to a tangent, and derivatives define tangents ....  find where the derivative is equal to the slope of the given line

anonymous · Answer

can you please just say the steps on how to solve it and i'll be the one to solve it...

amistre64 · Answer

those are the steps

anonymous · Answer

that only?

amistre64 · Answer

yep .... determine when the derivative is equal to the slope of the line;  this finds the point that you would need to use in a point slope form of the normal line equation

anonymous · Answer

i think i might get a hard time with that steps coz i'm new to this topic.. can you please elaborate further?

amistre64 · Answer

tell me what the slope of the given line is ...

anonymous · Answer

you can all help me :)

terenzreignz · Answer

^As soon as you're done with that. 
(What's the slope of the line given?)

anonymous · Answer

1/2

amistre64 · Answer

good,  then we will need to equate that to the derivative,  and also, the normal line will perp that slope.  what is the perpendicular slope of 1/2 ?  for future use

anonymous · Answer

-2

amistre64 · Answer

youre doing great;  lets form the normal line equation up so far:

(y-a) = -2(x-b) ... just need to define the point (a,b)  so lets move on to the derivative

what do you get as the derivaitve of the given curve?

amistre64 · Answer

the derivative of:   x^2 + 2y = 8  give it your best attempt

anonymous · Answer

2x + 2 y1 = 0
dy/dx = -x

amistre64 · Answer

good job ... so we need to determine when dy/dx = 1/2

-x = 1/2  when x=?

anonymous · Answer

-1/2

amistre64 · Answer

pretty simple eh :)

so we have part of our point (a,b) ...   (-1/2, b)

lets find b (the y value) by plugging in x=-1/2 into the curve

(-1/2)^2 + 2y = 8 ,  solve for y

anonymous · Answer

y = 31/8

amistre64 · Answer

marvolous ... so (a,b) = (-1/2, 31/8)

amistre64 · Answer

can you finish it from there?

anonymous · Answer

i just need to use point slope form right?

amistre64 · Answer

im not sure what format they want you to present it in, but yes ... the point slope form of a line is a line equation.

anonymous · Answer

i'm just finding the equation so that may be good.. thanks for the help! :)

amistre64 · Answer

youre welcome ;)