Hyperbola

Let equation of circle is
x2+y2 + 2ƒx + 2ƒy + e = 0, it passes through
(0, 2b)
⇒ 0 + 4b2 + 2g × 0 + 4ƒ + c = 0
⇒ 4b2 + 4ƒ + c = 0 ...(i)
2 √g2−c = 4a ... (ii)
g2 – c = 4a2 ⇒ c = (g2 - 4a2 )
Putting in equation (1)
⇒ 4b2 + 4ƒ + g2 – 4a2 = 0
⇒ x2 + 4y + 4(b2–a2) = 0, it represent a parabola.