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NDA 2019 Maths · Mathematics · Application of Derivatives · medium

The slope of the normal to the curve x^2+xy+y^2=7 at the point (1,2) is

Single correct option

The slope of the normal to the curve x2+xy+y2=7x^2+xy+y^2=7 at the point (1,2)(1,2) is
  1. A. 54\frac54
  2. B. −45-\frac45
  3. C. 45\frac45
  4. D. −54-\frac54
Show answer and solution

Answer: (A) 54\frac54

Differentiating implicitly, 2x+y+xy′+2yy′=02x+y+xy'+2yy'=0, so y′=−2x+yx+2yy'=-\frac{2x+y}{x+2y}. At (1,2)(1,2): y′=−45y'=-\frac{4}{5}. The normal's slope is the negative reciprocal, 54\frac54. The value −45-\frac45 is the slope of the tangent and not of the normal.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake