ax = 1+by – 2√ by
(ax–by–1)2 = (– 2 √ by)2
a2 x2 +b2 y2 +1–2abxy–2ax+2by = 4by
a2 x2 –2abxy+b2 y2 –2ax–2by+1 = 0
\(Δ= \begin{vmatrix}a^2&-ab&-a\\-ab&b^2&-b\\-a&-b&1\end{vmatrix}\)
= a2 (b2 –b2)+ab(–ab–ab) –a(ab2 +ab2)
= 0 – 2a2 b2 –2a2 b2
= – 4a2 b2 ≠ 0
h2 –ab = (–ab)2 – (a2) (b2) = 0
∴It is a parabola
