The line which is parallel to x -axis and crosses the curve y = x at an angle 45 ° , is

Step-by-step solution

The equation of a given curve is y = x ... i On diffrenciating the above equation with respect to x we get the slope ⇒ d y d x = 1 2 x The slope of the line at x 1 ,   y 1 ,   m 1 = 1 2 x 1 and let line parallel to x -axis is y = k ... ii Whose slope, 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 2 x 1 - 0 1 ⇒ x 1 = 1 4 ∴ y 1 = 1 2 [from Eq. i ] ∴ The required equation is y = 1 2 = k [from Eq. ii ]