Find the angle between the curves xy = 6 and x2y =12.

Solution :

The equation of the two curves are

xy = 6          …….(i)

and, x2y = 12            …………(ii)

from (i) , we obtain y = 6x. Putting this value of y in (ii), we obtain

x2 (6x) = 12 6x = 12

x = 2

Putting x = 2 in (i)  or (ii), we get y = 3.

Thus, the two curves intersect at P(2, 3).

Differentiating (i) with respect to x, we get

xdydx + y = 0 dydx = yx

m1 = (dydx)(2,3) = 32

Differentiating (ii) with respect to x, we get

x2 dydx + 2xy  = 0 dydx = 2yx

m2 = (dydx)(2,3) = -3

Let θ be the angle, then angle between angle between two curves

tanθ = m1m21+m1m2 = 311

θ = tan1(3/11)


Similar Questions

Find the equations of the tangent and the normal at the point ‘t’ on the curve x = asin3t, y = bcos3t.

Find the equation of the normal to the curve y = 2x2+3sinx at x = 0.

Find the equation of the tangent to curve y = 5x2+6x+7  at the point (1/2, 35/4).

Check the orthogonality of the curves y2 = x and x2 = y.

The angle of intersection between the curve x2 = 32y and y2 = 4x at point (16, 8) is

Leave a Comment

Your email address will not be published. Required fields are marked *