If the line x + y = k is a normal to the para | vedclass

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(C) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$.The equation of a normal to the parabola $y^2 = 4ax$ at point $(at^2, 2at)$

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$3$

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(C) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$.The equation of a normal to the parabola $y^2 = 4ax$ at point $(at^2, 2at)$ is $y = -tx + 2at + at^3$.Given the line is $x + y = k$,which can be written as $y = -x + k$.Comparing $y = -x + k$ with $y = -tx + 2at + at^3$,we get $t = 1$.Substituting $t = 1$ and $a = 1$ into the expression for $k$:$k = 2at + at^3 = 2(1)(1) + 1(1)^3 = 2 + 1 = 3$.Therefore,the value of $k$ is $3$.

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

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