Ellipse question

2009 · Shift 1 · Q30

Ellipse question

2009 · Shift 1 · Q30

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 $\|z+2\|-\|z-2\|=\pm3$ .
(C)	Ellipse	(R)	Points of the conic have parametric representation $x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$
(D)	Hyperbola	(S)	The eccentricity of the conic lies in the interval $1 \le x \le \infty$ .
		(T)	Points z in the complex plane satisfying ${\mathop{\rm Re} olimits} {(z + 1)^2} = \|z{\|^2} + 1$ .

A
(A) $\to$ (P); (B) $\to$ (S), (T); (C) $\to$ (R); (D) $\to$ (R), (S)
B
(A) $\to$ (P); (B) $\to$ (S), (T); (C) $\to$ (R); (D) $\to$ (Q), (S)
C
(A) $\to$ (P); (B) $\to$ (S), (T); (C) $\to$ (S); (D) $\to$ (R), (S)
D
(A) $\to$ (P); (B) $\to$ (P), (T); (C) $\to$ (R); (D) $\to$ (Q), (S)

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