Is there any other conic possible?

Question

It is told that a conic is the locus of all the points which satisfies the relation. $$\frac{SP}{PM}=constant$$

Where,

SP = distance of the point from fixed point

PM = distance of the point from fixed line

Which are of 6 types,

1. Point(s) (Finite)
2. Line(s)
3. Circle
4. Parabola
5. Ellipse
6. Hyperbola

Are these the only type of conic possible?

Answer 1

Actually there aren't, because we introduce these by cases for example as you said, $ 1) \ \Delta=0$ gives a line $\\$ $2) \ $ In $\Delta≠0$ we have cases,

$$(A) \ h²>ab, \ \ (B) \ \ h²=ab, \ \ (C) \ h²<ab$$

In each cases the locus was similar. So, we named each. For example $(A)$ gives hyperbola, $(B)$ gives parabola, $(C)$ gives ellipse and circle.