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AP EAMCET · Maths · Differential Equations

At any point x,y on a curve if the length of the subnormal is x-1 and the curve passes through 1,2 then the curve is a conic. A vertex of the curve is

  1. A 1,0
  2. B 0,1
  3. C 5,0
  4. D 1,2
Verified Solution

Answer & Solution

Correct Answer

(D) 1,2

Step-by-step Solution

Detailed explanation

Let the curve be y=fx Length of subnormal is given by ydydx i.e. ydydx=x-1 On integrating, we get y22=x22-x+C Given, the curve passes through 1,2 i.e. C=52 So, y2=x2-2x+5 or y24-x-124=1 is an equation of a hyperbola. Its vertex would lie on 1,±2