If the line x + y = 1 is a normal to the para | vedclass

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(B) The equation of the line is $y = -x + 1$,which is in the form $y = mx + c$,where $m = -1$ and $c = 1$. For a parabola $y^2 = 4ax$,the condition fo

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$4$

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(B) The equation of the line is $y = -x + 1$,which is in the form $y = mx + c$,where $m = -1$ and $c = 1$. For a parabola $y^2 = 4ax$,the condition for the line $y = mx + c$ to be a normal is $c = -2am - am^3$. Comparing $y^2 = kx$ with $y^2 = 4ax$,we get $4a = k$,so $a = k/4$. Substituting $m = -1$ and $c = 1$ into the condition: $1 = -2(k/4)(-1) - (k/4)(-1)^3$ $1 = (k/2) + (k/4)$ $1 = (2k + k) / 4$ $1 = 3k / 4$ $k = 4/3$.

If the line $x + y = 1$ is a normal to the parabola $y^2 = kx$,then find the value of $k$. (in $/3$)

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