The tangent to the curve $x y = 25$ at any point on it cuts the coordinate axes at A and B, then the area of the triangle OAB is

50 sq. units

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25 sq. units

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75 sq. units

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100 sq. units

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Solution

The correct option is D 50 sq. units
The tangent to $x y = 25$ at a point $(x_{1}, y_{1})$ can be written as $y = \frac{- y_{1}}{x_{1}} x + 2 y_{1}$
This would intersect the x axis at $(2 x_{1}, 0)$ and y axis at $(0, 2 y_{1})$
Thus, the area of the formed right angled triangle would be $\frac{1}{2} \times 2 x_{1} \times 2 y_{1}$
$= 2 x_{1} y_{1}$
$= 50$ sq unit

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The tangent to the curve xy=25 at any point on it cuts the coordinate axes at A and B, then the area of the triangle OAB is

The correct option is D 50 sq. unitsThe tangent to xy=25 at a point (x1,y1) can be written as y=−y1x1x+2y1This would intersect the x axis at (2x1,0) and y axis at (0,2y1)Thus, the area of the formed right angled triangle would be 12×2x1×2y1=2x1y1=50 sq unit

The tangent to the curve $x y = 25$ at any point on it cuts the coordinate axes at A and B, then the area of the triangle OAB is