If Ax - By -1 is a normal to the curve ay - x 2- thenA- 4 A 22- aB - aB 3B- 4 A 21- aB - aB 3C- 4 A 21- aB - aB 3D- 2 A 22- aB - aB 3

The correct option is D 2A^2 (2 aB) = aB^3 ay=x^2⇒ 1/ ( dy/dx )= a/2x_1= A/B ⇒ x_1=aB/2A and y_1=1/B a/2 Put (x_1, y_1) in ay = x^2 We get, 2A^2 (2 aB) = ...

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Standard XII

Mathematics

Subnormal

If Ax + By =1...

Question

If $A x + B y = 1$ is a normal to the curve $a y = x^{2}$ , then

$4 A^{2} (1 - a B) = a B^{3}$

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$4 A^{2} (2 + a B) = a B^{3}$

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$4 A^{2} (1 + a B) = a B^{3}$

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$2 A^{2} (2 - a B) = a B^{3}$

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Solution

The correct option is D
$2 A^{2} (2 - a B) = a B^{3}$

$a y = x^{2} \Rightarrow - \frac{1}{(\frac{d y}{d x})} = \frac{- a}{2 x_{1}} = - \frac{A}{B}$
$\Rightarrow x_{1} = \frac{a B}{2 A} a n d y_{1} = \frac{1}{B} - \frac{a}{2}$
Put $(x_{1}, y_{1}) i n a y = x^{2}$
We get, $2 A^{2} (2 - a B) = a B^{3}$

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If Ax+By=1 is a normal to the curve ay=x2, then

The correct option is D 2A2(2−aB)=aB3 ay=x2⇒−1(dydx)=−a2x1=−AB ⇒x1=aB2A and y1=1B−a2 Put (x1,y1)inay=x2 We get, 2A2(2−aB)=aB3

If $A x + B y = 1$ is a normal to the curve $a y = x^{2}$ , then