Question

The conic is represented by the equation $\sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1,(a>0,b>0),$ is

• A. circle
• B. parabola
• C. ellipse
• D. pair of straight line

Answer 1

The correct option is D pair of straight line

The conic is represented by equation $\sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1(a>0,b>0)$

${(\sqrt{bx}+\sqrt{ay})}^2={\left(\sqrt{ab}\right)}^{2}bx+ay+2\sqrt{abxy}=ab$

Let

$\sqrt{x}=m\sqrt{y}=nb{m}^2+a{n}^2+2\sqrt{ab}mn-ab=0\Delta =\left(b\right)\left(a\right)(-ab)-(-ab)\left(ab\right)=-a^2{b}^2+a^2{b}^2=0$

Hence they are pair of straight lines.