If (grad. of normal)(grad. of tangent)= -1, then why isn't (grad of x-axis)(grad. of y-axis)=1?

Question

How do i find a point on a curve whose normal is parallel to the x-axis?

Answer 1

(grad.of normal)(grad.of tangent)=-1 is true only if grad.of tangent is not zero.for the x axis the grad.is zero and the normal to the x-axis will be the y axis and therefore the product of the gradients of the x and the y axes cannot be -1 even though they are perpendicular to each other and the product of the grad.of perpendicular lines is -1.
if the normal is parallel to the x axis the slope of the normal will also be 0 and the equation of the normal will be y=c and so dy/dx=0.so differentiate the equation of the curve w.r.t. x and equate to 0 and solve to get the points

Answer 2

Assuming you have the equation of the curve, differentiate the curve with respect to the y axis (dx/dy). When the gradient with respect to the y axis is zero, the normal (which is at right angles) must be parallel to the x axis.

There are some curious answers previous to this one. Now you've got to decide which of us are mad and which are bad. Do you regret not listening to your teacher now?

Answer 3

A curve parallel to the x axis has the equation:
y=a

SO, (x,a) a point on that curve.

A line perpendicular to y=a is x=b
So, (b,y) is on this line.

Answer 4

First, can you tell me what is the gradient of y-axis. You would say infinity. But infinity is not a number. So you can't multiply it with anyother number. It becomes an indefinite form.

Answer 5

suppose your curve is described by (x(t),y(t))
then tangent is (x'(t),y'(t))
the normal is perpendicular on tangent
thus orthogonal vector n = (-y'(t),x'(t)).
( inproduct = 0 then orthogonal)
this vector n is paralelel with x-axis if x'(t) = 0. and y'(0)<>0
what yuo need to find is thus a t such that
x'(t) = 0, and y'(t)<>0

Answer 6

I'll have to get back to you on that. I'm busy tweezing my ear hairs right now.

Answer 7

ask goodwill hunting and john nash.