Implicit differentiate -C4

I am going crazy with this question:

A curve has the equation
x^2 + 3xy -2y^2 + 17 = 0

a) Find an express ion for (dy/dx) in terms of x and y

- This is what I got
2x + 3[x(dy/dx) + y] -4y(dy/dx) =0

hence: dy/dx = (-2x - 3y ) / (3x -4y)

b) Find an equation for the normal to the curve at the point (3, -2)

If i substitue x = 3 y = -2 into the equation grad = 0 hence normal = infinity.
Im pretty sure this is wrong but I can't see where I've made a mistake.
Help appreciated!!

Reply 1

yusufu

16

I get the same dy/dx as you.
the normal is therefore x = 3

Reply 2

Twiglet

2

If i substitue x = 3 y = -2 into the equation grad = 0 hence normal = infinity.
Im pretty sure this is wrong but I can't see where I've made a mistake.
Help appreciated!!

no, your're right , just remember if the gradient is infinity, the line is parallel to the y axis :smile:

- so the answer is as YYYY said

Reply 3

moleo

OP

ah i c now.
I just generally whenever infinity turns up in an answer i just tend to think its an error. :smile:

Reply 4

Twiglet

2

If: dy/dx = (-2x - 3y ) / (3x -4y)

subbing x = 3
y = -2
gives 0 as a numerator...?

yeah, so tangent gradient =0 and normal gradient=infinity, and now see my post above and YYYY's

Reply 5

yusufu

16

Think of gradient as up/across. so if the gradient is infinity, you're dividing by 0, so the line isnt moving across. Hence must be a vertical line.

Reply 6

gyrase

3

when you talk about gradients, you cant say the gradient is infinity. You have to say something like "the denominator is 0, so the gradient tends to infinity making a 90 degree angle with the x-axis, hence the normal/tangent is perpendicular to the x-axis and parallel to the y-axis."

Reply 7

yusufu

16

Dev.420

when you talk about gradients, you cant say the gradient is infinity. You have to say something like "the denominator is 0, so the gradient tends to infinity making a 90 degree angle with the x-axis, hence the normal/tangent is perpendicular to the x-axis and parallel to the y-axis."

Stick with vertical :p:

Implicit differentiate -C4

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