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  4. The slope of the tangent to the hyperbola 2x2 - 3y2 = 6 at (3, 2) is

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Q. The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is

BITSATBITSAT 2010

Solution:

Differentiating the given equation of the curve
$4 x-6 y .(d y / d x)= 0$
$\therefore d y / d x=2 x / 3 y$
$\left(\frac{d y}{d x}\right)_{(3,2)}=\frac{2}{3} \cdot \frac{3}{2}=1$