The line, which is parallel to `X`-axis and crosses the curve `y = sqrtx` at an angle `45^@`, is

Options

A. y=1/4
B. y=1/2
C. y=1
D. y=4

Answer

B

Explanation

The equation of given curve is ` y = sqrtx`

`Rightarrow (dy)/(dx) = 1/(2sqrtx)`
and let line parallel to X-axis be y = k
whose slope is `m_(2) =0 `
Since, `45^(@)` is the angle between the line and the curve
` tan 45^(@) |(m_(1) -m_(2))/(1+m_(1)m_(2))|`
` 1= |(1/(2sqrtx_(1))-0)/1|`
`Rightarrow x_(1) = 1/4`
Now, ` y_(1) = 1/2`
Hence, required line is y = `1/2`