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

Category: QuestionsWhat will be the equation of the normal to the hyperbola xy = 4 at the point (2, 2)?
Editor">Editor Staff asked 11 months ago

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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1 Answers
Editor">Editor Staff answered 11 months ago

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