Find the equation of the tangent to the curve y=x^2-2x that is perpendicular to the line 2y=x-1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the tangent to the curve y = x^2 - 2x that is perpendicular to the line 2y = x - 1 has to be found.

The line 2y = x - 1 can be written in the slope intercept form as y = (1/2)*x - 1/2. A line perpendicular to this has a slope -1/(1/2) = -2

For a function f(x), the value of f'(a) gives the slope of the tangent at the point x = a.

y = x^2 - 2x

y' = 2x - 2

If 2x - 2 = -2, x = 0 and subsequently y = 0

This gives the equation of the tangent as y/x = -2

=> y + 2x = 0

The equation of the tangent to the curve y=x^2 - 2x that is perpendicular to the line 2y = x - 1 is y + 2x = 0

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