Question

find the angle bětween the curves r= ax ÷ ( 1+x) , r= a÷ ( 1+x^2) at the point of intersection
​

Answer 1

Answer:

Given equation of curves are

y

2

=x and x

2

=y

first we have to find point of intersection

by equating both equations

x

4

=x

or, x

4

−x=0

⇒x(x

3

−1)=0

⇒x=0,x=1

at x=0,y=0; x=1,y=1

∴ point of intersection are (0,0) and (1,1)

Now, y

2

=2 and y=x

2

2y

dx

dy

=1 and

dx

dy

=2x

dx

dy

=

2y

1

⇒m

1

=

2

1

and

dx

dy

∣

∣

∣

∣

∣

x=1

=2

⇒m

2

=2

∴tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

2

−m

1

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1+

2

1

×2

2−

2

1

∣

∣

∣

∣

∣

∣

∣

∣

=

2

3/2

⇒tanθ=

4

3

⇒θ=tan

−1

3/4