Match the conics in Column I with the statements/expressions in Column II: Column I Column II (A) Circle (P) The locus of the point (h, k) for which the line hx + ky = 1 touches the circle x^2 + y^2 = 4. (B) Parabola (Q) Points z in the complex plane satisfying |z + 2| - |z - 2| = ±3. (C) Ellipse (R) Points of the conic have parametric representation x = \sqrt3(\frac{1-t^2}{1+t^2}) , y = \frac{2t}{1+t^2} (D) Hyperbola (S) The eccentricity of the conic lies in the interval 1 ≤ x ≤ ∞. (T) Points z in the complex plane satisfying Re(z +1)^2 = |z|^2 + 1. [JEE Adv 2009 P1]

Correct Answer is : (A)→(P); (B)→(S), (T); (C)→(R); (D)→(Q), (S)

(A)→(P); (B)→(S), (T); (C)→(R); (D)→(Q), (S)

(A)→(P); (B)→(R), (T); (C)→(R); (D)→(Q), (S)

(A)→(Q); (B)→(S), (T); (C)→(R); (D)→(P), (S)

(A)→(P); (B)→(R), (T); (C)→(R); (D)→(Q), (S)

Ellipse

Section: Mathematics

Question : 23 of 25

Marks: +1, -0

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

Column I

Column II

(A) Circle

(P) The locus of the point (h, k) for which the line hx + ky = 1 touches the circle x2+y2 = 4.

(B) Parabola

(Q) Points z in the complex plane satisfying |z + 2| - |z - 2| = ±3.

(R) Points of the conic have parametric representation x = √3(

1−t2

1+t2

) , y =

1+t2

(D) Hyperbola

(S) The eccentricity of the conic lies in the interval 1 ≤ x ≤ ∞.

(T) Points z in the complex plane satisfying Re(z+1)2 = |z|2 + 1.

[JEE Adv 2009 P1]

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