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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Indefinite Integration

BITSAT 2010 · Mathematics · Indefinite Integration

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

The slope of the tangent to the hyperbola 2x2−3y2=62 x²-3 y²=6 at (3,2)(3,2) is

Options

  1. A-1
  2. B1
  3. C0
  4. D2

Correct answer

B. 1

Step-by-step solution

Differentiating the given equation of the curve 4x−6y⋅(dy/dx)=0∴dy/dx=2x/3y(dydx)(3,2)=23⋅32=1\begin{aligned}& 4 x-6 y \cdot(\mathrm{dy}/ \mathrm{dx})=0 \quad \therefore \mathrm{dy}/ \mathrm{dx}=2 \mathrm{x}/ 3 \mathrm{y}\\ & \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{(3,2)}=\frac{2}{3}\cdot\frac{3}{2}=1 \end{aligned}
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