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

Question

Accepted Answer

Correct answer: B. (b) : xy=25, Let P (x_1 ,y_1 ) be point on the curve, slope (m ) at (x_1 ,y_1 )=- y_1x_1 Equation of tangent is y-y_1=- y_1x_1(x-x_1) ( x-intercept OA=a=2x_1 ,y-intercept OB=b=2y_1 ) Area of triangle OAB = 12 ab= 122x_12y_1=2 25=50 sq . units

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

Solution

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