Column $$I$$
(A) Circle
(B) Parabola
(C) Ellipse
(D) Hyperbola
Column $$II$$
(p) The locus of the point $$(h, k)$$ for which the line $$hx+ky=1$$ touches the circle $${x^2} + {y^2} = 4$$
(q) Points $$z$$ in the complex plane satisfying $$\left| {z + 2} \right| - \left| {z - 2} \right| = \pm 3$$
(r) Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),\,\,y = {{2t} \over {1 + {t^2}}}$$
(s) The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$
(t) Points $$z$$ in the complex plane satisfying $${\mathop{\rm Re}\nolimits} \,{\left( {z + 1} \right)^2}\, = {\left| z \right|^2} + 1$$
Column $$I$$
(A) Two intersecting circles
(B) Two mutually external circles
(C) Two circles, one strictly inside the other
(D) Two branches vof a hyperbola
Column $$II$$
(p) have a common tangent
(q) have a common normal
(r) do not have a common tangent
(s) do not have a common normal