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

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(B) The equation of a normal to the parabola $y^2 = 4ax$ at point $t$ is given by $y + tx = 2at + at^3$.Given $y^2 = 12x$,we have $4a = 12$,so $a = 3$

Vedclass · Accepted Answer

$9$

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(B) The equation of a normal to the parabola $y^2 = 4ax$ at point $t$ is given by $y + tx = 2at + at^3$.Given $y^2 = 12x$,we have $4a = 12$,so $a = 3$.The equation of the normal becomes $y + tx = 2(3)t + 3t^3$,which simplifies to $y + tx = 6t + 3t^3$.Comparing this with the given normal $x + y = k$,we have the coefficients of $x$ and $y$ proportional:$\frac{t}{1} = \frac{1}{1} \implies t = 1$.Substituting $t = 1$ into the constant term:$k = 6(1) + 3(1)^3 = 6 + 3 = 9$.

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

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