If the point P on the parabola y = x & # 178 is tangent L and the tangent L is perpendicular to the straight line 2x-y-5 = 0, then the equation of tangent L is,

It is known that the slope of the line 2x-y-5 = 0 is 2,
The slope of the line L is - 1 / 2
Let P (x0, x0 & # 178;)
y=x²
∴ y'=2x
The tangent slope is k = 2x0 = - 1 / 2
∴ x0=-1/4
The tangent point is (- 1 / 4,1 / 16)
The tangent equation is Y-1 / 16 = - (1 / 2) (x + 1 / 4)
The tangent equation is 8x + 16y + 1 = 0

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