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# Solution for The Curves Y = Aex And Y = Be−X Cut Orthogonally, If (A) A = B (B) A = −B (C) Ab = 1 (D) Ab = 2 - CBSE (Science) Class 12 - Mathematics

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#### Question

The curves y = aex and y = be−x cut orthogonally, if
(a) a = b
(b) a = −b
(c) ab = 1
(d) ab = 2

#### Solution

(c) ab = 1

$\text{ Given }:$

$y = a e^x . . . \left( 1 \right)$

$y = b e^{- x} . . . \left( 2 \right)$

$\text { Let the point of intersection of these two curves be }\left( x_1 , y_1 \right).$

$\text { Now,}$

$\text { On differentiating (1) w.r.t.x, we get }$

$\frac{dy}{dx} = a e^x$

$\Rightarrow m_1 = \left( \frac{dy}{dx} \right)_\left( x_1 , y_1 \right) = a e^{x_1}$

$\text { Again, on differentiating (2) w.r.t.x, we get }$

$\frac{dy}{dx} = - b e^{- x}$

$\Rightarrow m_2 = \left( \frac{dy}{dx} \right)_\left( x_1 , y_1 \right) = - b e^{- x_1}$

$\text { It is given that the curves cut orthogonally }.$

$\therefore m_1 \times m_2 = - 1$

$\Rightarrow a e^{x_1} \times \left( - b e^{- x_1} \right) = - 1$

$\Rightarrow ab = 1$

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#### Video TutorialsVIEW ALL [3]

Solution The Curves Y = Aex And Y = Be−X Cut Orthogonally, If (A) A = B (B) A = −B (C) Ab = 1 (D) Ab = 2 Concept: Tangents and Normals.
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