Question:
The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is
The slope of the tangent to the hyperbola $2x^2 - 3y^2 = 6$ at $(3, 2)$ is
Updated On: Jan 30, 2025
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The Correct Option is B
Solution and Explanation
Differentiating the given equation of the curve
$4 x-6 y .(d y / d x)= 0$
$\therefore d y / d x=2 x / 3 y$
$\left(\frac{d y}{d x}\right)_{(3,2)}=\frac{2}{3} \cdot \frac{3}{2}=1$
$4 x-6 y .(d y / d x)= 0$
$\therefore d y / d x=2 x / 3 y$
$\left(\frac{d y}{d x}\right)_{(3,2)}=\frac{2}{3} \cdot \frac{3}{2}=1$
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Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
