Question

Hey mates.... find the tangent drawn on y=x2 at x=0,x=1/2. also find the angle made by the x-axis. please solve this.

Answer 1

As y equal to 2 X is a straight line passing through origin so at x=0 or at x=1/2 or any other point its tangent will be the line itself

Answer 2

Explanation:

The required point be (x,y)

The tangent makes an angle of 45

o

with the x−axis.

∴ Slop of the tangent =tan45

o

=1

Since, the point lies on the curve.

Now, y=x

2

Differentiate w.r.t x,

⇒

dx

dy

=2x

Slop of the tangent =(

dx

dy

)

(x,y)

=2x

⇒ 2x=1 [ Given ]

⇒ x=

2

1

Now,

⇒ y=x

2

=(

2

1

)

2

=

4

1

∴ (x,y)=(

2

1

,

4

1

)