"If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a $\\ne$ 0, then 'a' must be greater than :"

"Let the equation of the normal is y = mx $-$ 2am $-$ am 3 here 4a = 2 $\\Rightarrow$ a = ${1 \\over 2}$ y = mx $-$ m $-$ ${1 \\over 2}$m 3 It passing through A(a, 0) then 0 = am $-$ m $-$ ${1 \\over 2}$m 3 m = 0, a $-$ 1 $-$ ${1 \\over 2}$m 2 = 0 m 2 = 2(a $-$ 1) > 0 $\\Rightarrow$ a > 1"

Medium MCQ +4 / -1 PYQ · JEE Mains 2021

If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a $\ne$ 0, then 'a' must be greater than :

A ${1 \over 2}$
B 1 Correct answer
C $-$1
D $-$${1 \over 2}$

Solution

Let the equation of the normal is y = mx $-$ 2am $-$ am3 here 4a = 2 $\Rightarrow$ a = ${1 \over 2}$ y = mx $-$ m $-$ ${1 \over 2}$m3 It passing through A(a, 0) then 0 = am $-$ m $-$ ${1 \over 2}$m3 m = 0, a $-$ 1 $-$ ${1 \over 2}$m2 = 0 m2 = 2(a $-$ 1) > 0 $\Rightarrow$ a > 1

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Subject: Mathematics · Chapter: Conic Sections · Topic: Parabola

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If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a $\ne$ 0, then 'a' must be greater than :

Solution

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If the three normals drawn to the parabola, y² = 2x pass through the point (a, 0) a $\ne$ 0, then 'a' must be greater than :