The number of normals drawn to the parabola y | vedclass

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(B) The equation of the parabola is $y^2=4ax$,where $a=1$. The point $(1,0)$ is the focus of the parabola.Any normal to the parabola $y^2=4ax$ at poin

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$1$

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(B) The equation of the parabola is $y^2=4ax$,where $a=1$. The point $(1,0)$ is the focus of the parabola.Any normal to the parabola $y^2=4ax$ at point $(at^2, 2at)$ is given by the equation $y = -tx + 2at + at^3$.If this normal passes through the point $(h, k) = (1, 0)$,then $0 = -t(1) + 2(1)t + (1)t^3$.This simplifies to $0 = t + t^3$,or $t(1 + t^2) = 0$.The real solution for $t$ is $t=0$.For $t=0$,the normal is $y = 0$,which is the $x$-axis.Thus,only $1$ normal can be drawn from the point $(1,0)$ to the parabola $y^2=4x$.

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is

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