Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaNormal to ParabolaMedium2 minQB

MathematicsMediuminteger

The number of distinct normals, which can be drawn from the point $(2, 8)$ to the parabola $y^{2} = 6 x$ is

Answer:

Solution:

Any normal will be $y + tx = 3 t + \frac{3}{2} t^{3}$ , it passes through (2, 8), so $3 t^{3} + 2 t - 16 = 0$ Let $f (t) = 3 t^{3} + 2 t - 16$ $\Rightarrow f^{'} (t) = 9 t^{2} + 2 < 0,$ So only one normal.

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Normal to Parabola

⏱ 2mℹ️ Source: QB

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