Which conic section does z represent?

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If a,b,c,d are four complex numbers such that $c/d$ is real and ad-bc is not equal to 0.z is defined as $\dfrac{a+bt}{c+dt}$ where t is a real number.Which conic section does z represent?

My approach:

$\dfrac{a+bt}{c+dt} =\dfrac{b(a/b+t)}{d(c/d+t)} = b/d,$ if $(ad-bc)=0$.

That would represent a single point in the Argand plane.What's next?