If the line y = -x + k is normal to the curve | vedclass

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(D) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $a = 4$.The equation of the normal to the parabola $y^2 = 4ax$

Vedclass · Accepted Answer

$12$

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(D) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $a = 4$.The equation of the normal to the parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx - 2am - am^3$.Substituting $a = 4$,the normal is $y = mx - 8m - 4m^3$.Given that the line $y = -x + k$ is a normal,we compare the slopes: $m = -1$.Substituting $m = -1$ into the equation of the normal:$y = (-1)x - 8(-1) - 4(-1)^3$$y = -x + 8 + 4$$y = -x + 12$Comparing this with $y = -x + k$,we get $k = 12$.

If the line $y = -x + k$ is normal to the curve $y^2 = 16x$,then $k$ is

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