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JEE Advanced2009MathematicsHyperbolaActual

Match the conics in Column I with the statements/expressions in Column II.

Options

  1. A(A) s, (B) q,s, (C) s, (D) p,s
  2. B(A) p, (B) q,s, (C) r, (D) q,s
  3. C(A) s, (B) s,t, (C) s, (D) p,s
  4. D(A) p, (B) s,t, (C) r, (D) q,s

Correct answer

D. (A) p, (B) s,t, (C) r, (D) q,s

Step-by-step solution

(p) 1 h^2+k^2 =2 h^2+k^2= 1 4 Hence, locus is a circle. (q) || z+2|-| z-2||=3 and 2-(-2)=4>3 Hence, locus is hyperbola. (r) Let x= 3 ( 1-t^2 1+t^2 ), y= 2 t 1+t^2 Let =t x= 3 2 , y= 2 x^2 3 +y^2=1 Hence, locus is an ellipse. (s) Eccentricity x=1 Parabola, 1 < x < Hyperbola (t) Let z=x+i y Since, Re (z+1)^2=|z|^2+1 (x+1)^2-y^2=x^2+y^2+1 2 x=2 y^2 x=y^2 Hence, locus is parabola.

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