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