The angle between the tangents drawn from the point `(1,4)` to the parabola `y^2=4x` is

Options

A. 0
B. `pi//6`
C. `pi//4`
D. `pi//3`

Answer

A

Explanation

Given curve, `y^(2)=4x` . . . (i)
and `x^(2)=4y` . . . (ii)
from Eq. (i) `2y(dy)/(dx)=4implies(dy)/(dx)=(2)/(y)`
`implies((dy)/(dx))_((1,4))=(2)/(4)=(1)/(2)=m_(1)`
Now, from eq. (ii)
`2x=4(dy)/(dx)implies(dy)/(dx)=(x)/(2)`
`implies((dy)/(dx))_((1,4))=(1)/(2)=m_(2)`
`becausem_(1)=m_(2)`
so, tangents are parallel.