$y^2=(x-a)(x-b)^2\;a ,b > 0, a >b$

Step 1:

Existence : The curve does not exist for $x < a$

$\therefore $ it does not exist for $ -\infty < x < a$ except at $x=b( b < a)$ when $y=0$

The curve exists for $ a \leq x < \infty$

Step 2:

(ii) Symmetry: The curve is symmetric about x-axis only

Step 3:

(iii) Asymptotes: The curve does not admit asymptotes since there are no further values of $ x(or\;y)$ for which $y \to \pm \infty(or\; x \to \pm \infty)$

Step 4:

Loops:The curve passes through (0,0) twice but no loop is formed because the curve does not exist for $ b \leq x < a$