Differentiation. I need help for part (b)

[astral rock]

why is your paper black

[heavy marsh]

racist

jk

I inverted the colours on pc white too bright

[magic parrot]

dy/dx＝(dy/dt)/(dx/dt)

[heavy marsh]

yup part (b) im stuck

[magic parrot]

hmmm, had u find the point when cost＝3/4?

[heavy marsh]

how do you find that

[magic parrot]

just put that in

[heavy marsh]

p is unknown

[magic parrot]

"p is a positive constant" as the question just said

not an unknown

[formal glen]

sin^2 + cos^2 = 1. You can deduce the value of sin(t) at R

also, that should be unecessary, anyway, you have dy / dx

at R, it should be -3

[formal glen]

Ye, but that doesn't tell you anything about the normal

only the values of x and y

dy / dx should give the tangent

[heavy marsh]

that y im stuck

[formal glen]

and you know how to get the normal from the tangent

[heavy marsh]

got grad of normal tho

I need to find coordinates of pt R

[formal glen]

You can't, it depends on p

but you don't need the coordinates of R

you want the normal to the curve, which is a line orthogonal to it at point R

aka, orthogonal to the tangent

And knowing dy/dx, how should you find the tangent?

[heavy marsh]

I need a Point?

[formal glen]

Sure, the point is R

what is the value of dy/dx at R?

[heavy marsh]

-3

[formal glen]

Deduce the slope of the tangent line to this curve, at point R, then

It's neat, because we don't know where the point is, but regardless, we always know the slope at that point (because you kind of scale the whole figure when you multiply with p, see?)

[heavy marsh]

wdym by slope isnt it same thing as gradient

[formal glen]

you mean dy/dx?

ye, that is the slope

but then you need to write it as an equation, in terms of x and y

[heavy marsh]

howw

[formal glen]

well, it's a line with slope dy/dx at R, so the slope is -3

what's the equation for a line with slope -3? (suppose that it passes through the origin)

[heavy marsh]

where did it mention passing through origin

[formal glen]

it doesn't, just a hypothesis for the sake of simplicity

I mean, if you have the equation of a line passing through the origin, you just need to add a constant to get it to change its starting point

y = ax -> y = ax + b

[heavy marsh]

yeah right

[formal glen]

a is the slope, so here y = -3x, would be the equation of the tangent, (if it were passing through the origin). Now it only remains to find the slope of the normal (just flip this line and take the new slope), then find the offset b in ax + b

[heavy marsh]

do you have the answer