Question

The equation $5x^2+y^2+y=8$ represents

• A. an ellipse
• B. a parabola
• C. a hyperbola
• D. a circle
• E. a straight line

Answer 1

Answer: (A)

We have,
$5x^2+y^2+y=8$
$\Rightarrow 5x^2+(y+1/2{)}^2-{\left(\frac{1}{2}\right)}^2=8$
$\Rightarrow 5x^2+{\left(y+\frac{1}{2}\right)}^2=\frac{33}{8}$
$\Rightarrow \frac{5x^2}{\frac{33}{8}}+\frac{(y+1/2{)}^2}{\frac{33}{8}}=1$
$\Rightarrow \frac{x^2}{\left(\frac{33}{40}\right)}+\frac{(y+1/2{)}^2}{\left(\frac{33}{8}\right)}=1$
which is an equation of ellipse.