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Assertion (A) : The curves $y = x^{2}, 6 y = 7 - x^{3}$ cut orthogonally at $(1, 1)$
Reason (R) :Two curves cut each other orthogonally at their point of intersection ‘p’ iff $m_{1} m_{2} = - 1,$ where $m_{1}, m_{2}$ are gradients of the two curves at p

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a

A is false, R is true

b

A is true, R is false

c

A is true, R is true R is a correct explanation for A

d

A is true, R is true but R is not correct explanation of A

answer is A.

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Detailed Solution

$\begin{array}{l} A : \frac{dy}{dx} = 2 x \\ m_{1} = {(\frac{dy}{dx})}_{(1, 1)} = 2 \\ 6 \frac{dy}{dx} = - 3 x^{2} \\ \frac{dy}{dx} = \frac{- x^{2}}{2} \\ m_{2} = {(\frac{dy}{dx})}_{(1, 1)} = - \frac{1}{2} \\ m_{1} m_{2} = 2 \times - \frac{1}{2} = - 1 \end{array}$
$∴$ Given curves intersect orthogonally at (1, 1)
A is true, R is true R in correct explanation of A

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Assertion (A) : The curves y=x2, 6y=7−x3 cut orthogonally at (1, 1)Reason (R) :Two curves cut each other orthogonally at their point of intersection ‘p’ iff m1m2=−1, where m1, m2 are gradients of the two curves at p