If x + y = K is a normal to the parabola y^2 | 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 given line is $x + y = K$,which can b

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 given line is $x + y = K$,which can be written as $y = -x + K$. The slope of this line is $m = -1$.The equation of a normal to the parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx - 2am - am^3$.Substituting $a = 3$ and $m = -1$ into the equation:$y = (-1)x - 2(3)(-1) - (3)(-1)^3$$y = -x + 6 + 3$$y = -x + 9$$x + y = 9$Comparing this with $x + y = K$,we get $K = 9$.

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

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