Match the conics in Column I with the statements/expressions in Column II. Column I (A) Circle (B) Parabola (C) Ellipse (D) Hyperbola Column II (p) The locus of the point $( h , k )$ for which the line $h x + k y = 1$ touches the circle $x ^ { 2 } + y ^ { 2 } = 4$ (q) Points $z$ in the complex plane satisfying $| z + 2 | - | z - 2 | = \pm 3$ (r) Points of the conic have parametric representation $x = \sqrt { 3 } \left( \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } } \right) , y = \frac { 2 t } { 1 + t ^ { 2 } }$ (s) The eccentricity of the conic lies in the interval $1 \leq x < \infty$ (t) Points $z$ in the complex plane satisfying $\operatorname { Re } ( z + 1 ) ^ { 2 } = | z | ^ { 2 } + 1$
A - (p); B - (t); C - (r); D - (q, s)
Match the conics in Column I with the statements/expressions in Column II.
\textbf{Column I}\\
(A) Circle\\
(B) Parabola\\
(C) Ellipse\\
(D) Hyperbola
\textbf{Column II}\\
(p) The locus of the point $( h , k )$ for which the line $h x + k y = 1$ touches the circle $x ^ { 2 } + y ^ { 2 } = 4$\\
(q) Points $z$ in the complex plane satisfying $| z + 2 | - | z - 2 | = \pm 3$\\
(r) Points of the conic have parametric representation $x = \sqrt { 3 } \left( \frac { 1 - t ^ { 2 } } { 1 + t ^ { 2 } } \right) , y = \frac { 2 t } { 1 + t ^ { 2 } }$\\
(s) The eccentricity of the conic lies in the interval $1 \leq x < \infty$\\
(t) Points $z$ in the complex plane satisfying $\operatorname { Re } ( z + 1 ) ^ { 2 } = | z | ^ { 2 } + 1$