Application of Derivatives

Find the angle of intersection between 2 curves : $y^2 = 4x$ and $x^2 = 4y$ .

Question

Application of Derivatives

Find the angle of intersection between 2 curves : $y^2 = 4x$ and $x^2 = 4y$ .

mathslover · Answer

@ganeshie8

ganeshie8 · Answer

the two curves intersect at (0, 0) and (4, 4)

mathslover · Answer

Yeah.

ganeshie8 · Answer

angle of intersection at (0,0) is trivial - horizontal/vertical tangents - that means angle between them is 90 degrees

mathslover · Answer

Oh...

mathslover · Answer

Fine now. I can continue from here!

ganeshie8 · Answer

find the tangents at (4, 4) and find the angle between them.... or do u have any shortcut formula for this also ? :)

mathslover · Answer

Well, dy/dx = 4/2y (from y^2 = 4x)

At (4,4) (dy/dx) =  4/8 = 1/2 = m1

and At (0,0) (dy/dx) = 4/0 = infinity 

Also, dy/dx = x/2 (from x^2 = 4y) 

At (4,4) (dy/dx) = 4/2 = 2 = m2

and at (0,0) dy/dx = 0

mathslover · Answer

Angle between 2 curves :

$\tan \theta = \cfrac{m_1 - m_2}{1 + m_1 m_2 }$ 

Theta = tan^{-1} (3/4)

mathslover · Answer

that is not a shortcut but yes, that is what I know yet :)

ganeshie8 · Answer

yes i would do it the exact same way :)

mathslover · Answer

Great then. Thanks again :)

mathslover · Answer

Good Night Bhaiya! :-)

ganeshie8 · Answer

this also works : http://www.wolframalpha.com/input/?i=arctan%282%29+-+arctan%281%2F2%29+

ganeshie8 · Answer

good night, have good sleep :)

mathslover · Answer

After getting such kind of help, I will surely have a sound sleep. :) Gn