A tangent is drawn to the parabola y^{2}=6x w | vedclass

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(C) The given parabola is $y^{2}=6x$,so $4a=6$,which implies $a=\frac{3}{2}$.The slope of the line $2x+y=1$ is $m_{L}=-2$.Since the tangent is perpend

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$(5,4)$

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(C) The given parabola is $y^{2}=6x$,so $4a=6$,which implies $a=\frac{3}{2}$.The slope of the line $2x+y=1$ is $m_{L}=-2$.Since the tangent is perpendicular to this line,its slope $m$ satisfies $m 	imes (-2) = -1$,so $m=\frac{1}{2}$.The equation of the tangent to the parabola $y^{2}=4ax$ with slope $m$ is $y=mx+\frac{a}{m}$.Substituting $a=\frac{3}{2}$ and $m=\frac{1}{2}$,we get $y=\frac{1}{2}x+\frac{3/2}{1/2} = \frac{1}{2}x+3$.Multiplying by $2$,we get $2y=x+6$,or $x-2y+6=0$.Now,check the given points:For $(-6,0)$: $-6-2(0)+6=0$ (Lies on it).For $(4,5)$: $4-2(5)+6=4-10+6=0$ (Lies on it).For $(5,4)$: $5-2(4)+6=5-8+6=3 
eq 0$ (Does $NOT$ lie on it).For $(0,3)$: $0-2(3)+6=0$ (Lies on it).Thus,the point $(5,4)$ does not lie on the tangent.

$A$ tangent is drawn to the parabola $y^{2}=6x$ which is perpendicular to the line $2x+y=1$. Which of the following points does $NOT$ lie on it?

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