JEE Advanced2009MathematicsHyperbolaActual
Match the conics in Column I with the statements/expressions in Column II.
Options
- A(A) s, (B) q,s, (C) s, (D) p,s
- B(A) p, (B) q,s, (C) r, (D) q,s
- C(A) s, (B) s,t, (C) s, (D) p,s
- 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.