On the parabola y = x^2,the point at the leas | vedclass

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(A) The shortest distance between a curve and a line occurs at a point where the tangent to the curve is parallel to the given line.Given the parabola

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$(1, 1)$

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(A) The shortest distance between a curve and a line occurs at a point where the tangent to the curve is parallel to the given line.Given the parabola $y = x^2$,the slope of the tangent at any point $(x, y)$ is given by $\frac{dy}{dx} = 2x$.The given line is $y = 2x - 4$,which has a slope of $2$.For the tangent to be parallel to the line,we set the slope of the tangent equal to the slope of the line:$2x = 2 \Rightarrow x = 1$.Substituting $x = 1$ into the parabola equation $y = x^2$,we get $y = (1)^2 = 1$.Thus,the point on the parabola closest to the line is $(1, 1)$.

On the parabola $y = x^2$,the point at the least distance from the straight line $y = 2x - 4$ is

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