Question

The curve represented by √ax + √by  = 1, where a, b > 0 is

(a)  a circle 

(b)  a parabola

(c)  an ellipse

(d)  a hyperbola

Answer 1

Correct option   (b) a parabola

Explanation:

ax = 1 + by – 2√by

(ax – by – 1)² = (-2√by)²

a²x² + b²y² + 1 – 2abxy – 2ax + 2by = 4by

a²x² – 2abxy + b²y²– 2ax – 2by + 1 = 0

= a² (b² – b² ) + ab( – ab – ab)  – a(ab² + ab² )

= 0 – 2a²b² –2a²b²

=  – 4a² b² ≠ 0 

h²– ab = (–ab)² – (a²) (b²) = 0

It is a parabola