Finding two possible coordinates of a line parallel to the tangent

Original post by Mysticmeg

There's this last question that I'm stuck on in my maths assignment.

Here's the question (I've done the first part):

a) Find the equation of the tangent to f(x)=1/4x at the point x=2
Answer: x +16y - 4 =0

b)At the point R, the tangent to f(x)=1/4x is parallel to the line
x + 4y + 12 =0. Find the two possible coordinates of R.

Could someone explain how you find co-ordinates of a parallel line, I only know perpendicular (-1/m)

Parallel is even simpler: the gradients of the two lines have to be the same :smile:

Reply 2

OP

Original post by davros

Parallel is even simpler: the gradients of the two lines have to be the same :smile:

Do i need to rearrange to:
x+ 4y + 12 = 0 --------------- > y= -4 -x/4
x + 18y - 4 = 0 ----------------> y= 1/4 - x/16

(I don't really know what I'm doing)
I think I'm over complicating things

Reply 3

Original post by Mysticmeg

Do i need to rearrange to:
x+ 4y + 12 = 0 --------------- > y= -4 -x/4
x + 18y - 4 = 0 ----------------> y= 1/4 - x/16

(I don't really know what I'm doing)
I think I'm over complicating things

No, first work out what the gradient of the line x + 4y + 12 = 0 is - that tells you what you're aiming for.

Use differentiation to find what the gradients of 1/(4x) is at a a general point - you should have done this already!

Now you can work out the points where the tangents have to be.

(edited 9 years ago)

Reply 4

OP

Original post by davros

No, first work out what the gradient of the line x + 4y + 12 = 0 is - that tells you what you're aiming for.

Use differentiation to find what the gradients of 1/(4x) is at a a general point - you should have done this already!

Now you can work out the points where the tangents have to be.

For the gradient of 1/(4x) I got dy/dx= (1/4)(x)^-2 and for the tangent of that -1/16

I've honestly forgotten how to work out the gradient of a straight line... :colondollar:

When I tried I ended up with y= (-1/4)x - 3

Reply 5

Hasufel

re-arrange the line to be in slope intercept form.

this shows it`s gradient.

as this gradient has to be equal to that of the tangents to the curve, differentiate the curve and equate it to the gradient of the line you re-arranged.

2 values = 2 tangents

use x values to work out y values.....

(edited 9 years ago)

Reply 6

Hasufel

your straight line is correct, but your dy/dx should be (-1/4) as you are multiplying by the index -1

Reply 7

Original post by Mysticmeg

For the gradient of 1/(4x) I got dy/dx= (1/4)(x)^-2 and for the tangent of that -1/16

I've honestly forgotten how to work out the gradient of a straight line... :colondollar:

When I tried I ended up with y= (-1/4)x - 3

You're making this too difficult for yourself!

If ax + by + c = 0 then you can rearrange this to get by = -ax - c or
y = (-a/b)x - (c/b)

so the gradient of the line is just -a/b.

Your derivative should be -1/(4x^2).

So you just need the 2 values of x where the derivative equals the gradient :smile:

Reply 8

OP

Original post by davros

You're making this too difficult for yourself!

If ax + by + c = 0 then you can rearrange this to get by = -ax - c or
y = (-a/b)x - (c/b)

so the gradient of the line is just -a/b.

Your derivative should be -1/(4x^2).

So you just need the 2 values of x where the derivative equals the gradient :smile:

I've managed to get one set of co ordinates (-1, -1/4)
by working out the gradient of x + 4y + 12 = 0

How to i get the second set i tried doing th same for x + 16y - 4 but ended up with a gradient of 236...

Reply 9

Original post by Mysticmeg

I've managed to get one set of co ordinates (-1, -1/4)
by working out the gradient of x + 4y + 12 = 0

How to i get the second set i tried doing th same for x + 16y - 4 but ended up with a gradient of 236...

Why are you doing stuff with x + 16y - 4 - that's the first part of the question and is irrelevant!

If your gradient is -1/4 and your derivative is -1/(4x^2) you are looking for the values of x that make these two equal :smile:

Reply 10

OP