If x+y=k is a normal to the parabola y^{2}=12 | vedclass

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(B) The equation of the parabola is $y^{2}=12x$. Comparing this with $y^{2}=4ax$,we get $4a=12$,so $a=3$.The equation of a normal to the parabola $y^{

Vedclass · Accepted Answer

$9$

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(B) The equation of the parabola is $y^{2}=12x$. Comparing this with $y^{2}=4ax$,we get $4a=12$,so $a=3$.The equation of a normal to the parabola $y^{2}=4ax$ at point $(at^{2}, 2at)$ is $y = -tx + 2at + at^{3}$.Given the normal is $x+y=k$,which can be written as $y = -x + k$.Comparing $y = -tx + 2at + at^{3}$ with $y = -x + k$,we get $t=1$.Substituting $t=1$ and $a=3$ into the expression for $k$:$k = 2at + at^{3} = 2(3)(1) + 3(1)^{3} = 6 + 3 = 9$.Therefore,$k=9$.

If $x+y=k$ is a normal to the parabola $y^{2}=12x$,then the value of $k$ is:

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