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 focus of the parabola is $(a, 0) = (1, 0)$.Any normal to the parabola $y^2 = 4ax$ a

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$1$

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(B) The equation of the parabola is $y^2 = 4ax$,where $a = 1$. The focus of the parabola is $(a, 0) = (1, 0)$.Any normal to the parabola $y^2 = 4ax$ at point $(at^2, 2at)$ is given by $y = -tx + 2at + at^3$.Since the normal passes through $(1, 0)$,we substitute $x = 1$ and $y = 0$ into the equation:$0 = -t(1) + 2(1)t + (1)t^3$$0 = -t + 2t + t^3$$0 = t + t^3$$t(1 + t^2) = 0$Since $t$ must be a real number,the only solution 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.

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

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