More implicit diff.

[jsbeckton]

Have a question that has me a bit confused, its been awhile since I did implicit differentiation.

Show that the equation of the tangent line to the parabala y^2 = 4px at the point (Xo,Yo) can be written as YoY=2p(X+Xo)

Heres what I have:

y^2 = 4px

d/dx [y(x)^2] = d/dx [4px]

2y dy/dx = 4p

dy/dx = 2p/y

point = (Xo,Yo)
slope = 2p/y

eqn: Y-Yo=2p/y (X-Xo)
Y(Y-Yo) = 2p (X-Xo)
Y^2 - YYo = 2p (X-Xo)

my problem is that the left side of my equation dose not equal the left side of his and Y^2-YY0 cannot be converted to YYo.

Any suggestions would be greatly appreciated, thanks.

 

[stapel]

You have, from the original equation, that y² = 4px. You have found, through implicit differentiation, that y² - yy₀ = 2p(x - x₀). Substituting, we get:

. . . . .4px - yy₀ = 2p(x - x₀)

. . . . .4px - yy₀ = 2px - 2px₀

. . . . .4px - 2px + 2px₀ = yy₀

. . . . .2px + 2px₀ = yy₀

. . . . .2p(x + x₀) = yy₀

So you were almost there. :wink:

Hope that helps a bit.

Eliz.

P.S. Thank you for showing all of your steps!

 

[jsbeckton]

Thanks alot, I feel so stupid that I never tought of that. I was thinking outside the box when I should have been thinking inside!