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NDA 2018 Maths · Mathematics · Derivatives · easy

The slope of the tangent to the circle x^2+y^2=25 at the point (3,4) is

Single correct option

The slope of the tangent to the circle x2+y2=25x^2+y^2=25 at the point (3,4)(3,4) is
  1. A. −34-\frac34
  2. B. 34\frac34
  3. C. −43-\frac43
  4. D. 43\frac43
Show answer and solution

Answer: (A) −34-\frac34

Differentiating implicitly, 2x+2ydydx=02x+2y\frac{dy}{dx}=0, so dydx=−xy=−34\frac{dy}{dx}=-\frac xy=-\frac34. The tangent is perpendicular to the radius, whose slope is 43\frac43; the value −43-\frac43 confuses the two.
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Original question written in the NDA 2018 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