Question

The name of the conic represented by $\sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1$ is

• A. Circle
• B. Parabola
• C. Ellipse
• D. Hyperbola

Answer 1

Answer: (B)

Parabola

$\sqrt{x/a}+\sqrt{y/b}=1$

rearranging : $\sqrt{y/b}=1-\sqrt{x/a}$

squaring $y/b=1+x/a-2\sqrt{x/a}$

$\Rightarrow 2\sqrt{x/a}=1+x/a-y/b$

squaring again

$4x/a=1+x^2/a^2+y^2/b^2+2x/a-\frac{2xy}{ab}-\frac{2y}{b}$

Generally, when there is an equation of the form $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$, if $B^2-4AC=0$, then the centre is one of the following:

(1) A parabola

(2) $2$ parallel lines ( certainly this is not the case)

(3) $1$ line ( certainly this is not the case)

(4) No curve ( again not the case).

$\therefore \sqrt{x/a}+\sqrt{y/b}=1$ is a part of a parabola