Question

name the conic represented by the equation √ax + √by = 1​

Answer 1

√ax+√by=1

Squaring both the sides

ax+by+√2axby=1

ax+by -1= -√2axby

Squaring both sides

(ax+by-1)^2=4axby

a²x²+b²y²+1-2ax-2abxy-2by=0

A=a², B=b²,C=0, F= -b, G= -a, H= -ab

∆=ABC+2FGH-AF²-BG²-CH²

∆= 0-2a²b²-a²b²-b²a²

∆= -4a²b²

∆×=0, and H²=AB.

There fore it is a parabola