What will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?

(a) x + y = 0

(b) x – y = 0

(c) 2x – y = 0

(d) x + 2y = 0

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The question is from Calculus Application in chapter Application of Calculus of Mathematics – Class 12

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Correct answer is (b) x – y = 0

The best I can explain: Equation of the given hyperbola is, xy = 4 ……….(1)

Differentiating both side of (1) with respect to y, we get,

y*(dx/dy) + x(1) = 0

Or dx/dy = -(x/y)

Thus, the required equation of the normal to the hyperbola at (2, 2) is,

y – 2 = -[dx/dy](2, 2) (x – 2) = -(-2/2)(x – 2)

So, from here,

y – 2 = x – 2

Or x – y = 0