Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaNormal to ParabolaEasy2 minQB

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If the line $y = 2 x + k$ is normal to the parabola $y^{2} = 4 x$ , then value of k equals

Answer:

Solution:

The normal of slope $m$ to $y^{2} = 4 a x$ is $y = m x - 2 am - a m^{3}$ . Here $a = 1, m = 2$ .

So the normal is $y = 2 x - 4 - 8 = 2 x - 12$ , giving $k = - 12$ .

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Normal to Parabola

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