Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaNormal to ParabolaEasy2 minQB

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The number of normals that can be drawn to the parabola y² = 4x from the point (1, 0) is

Answer:

Solution:

The normal at the point $t$ on $y^{2} = 4 x$ is $y = - t x + 2 t + t^{3}$ .

It passes through $(1, 0)$ : $0 = - t + 2 t + t^{3} = t (t^{2} + 1)$ , so $t = 0$ is the only real value.

Note $(1, 0)$ is the focus of this parabola; the only normal through it is the axis itself. Hence the number of normals is $1$ .

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Normal to Parabola

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