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AP EAMCET20225 Jul 2022Evening ShiftMathematicsHyperbolaActual

If the line a x+b y+c=0 is a normal to the curve x y=1 , then

Options

  1. Aa>0, b>0
  2. Ba>0, b < 0
  3. Ca>0, b=0
  4. Da < 0, b < 0

Correct answer

B. a>0, b < 0

Step-by-step solution

Given curve is x y=1 So, y= 1 x ...(i) Differentiating with respect to x , we get, x d y ~d x +y=0[ (u v) =u v +u v] d y ~d x =- y x Given line is, a x+b y+c=0 The slope of a line is the coefficient of x in y=m x+c form. Thus, the slope of the given line is, - a b Thus the slope of tangent is, b a , [ . slope of normal .=- 1 slope of line ] Since the slope is normal to the curve, the normal of the line will be tangent to the curve. Thus, - y x = b a - 1 x x = b a [ y= 1 x ] So, LHS will always be a positive value,

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