Correct option (b),(c)
Explanation :
The normal at P(x1, y1) is
y - y1 = -1/m(x - x1)
where
m(dy/dx)(x1,y1)
Now, y = 0 ⇒ x1 + my1 + my1 so that by hypothesis, we have
|x1 + my1| = 2|x1|
Therefore, x1 + my1 = ±2x1.
which is a hyperbola.
which is an ellipse.