The equation 5 x^2+y^2+y=8 represents - Vidyadip

MCQ

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

✓
an ellipse
B
a parabola
C
a hyperbola
D
a circle

✓

Answer

Correct option: A.

an ellipse

(A)
$5 x^2+y^2+y=8$
$\Rightarrow 5 x^2+y^2+y+\frac{1}{4}=8+\frac{1}{4}$
$\Rightarrow 5 x^2+\left(y+\frac{1}{2}\right)^2=\frac{33}{4}$
$\Rightarrow \frac{x^2}{\left(\frac{33}{20}\right)}+\frac{\left(y+\frac{1}{2}\right)^2}{\left(\frac{33}{4}\right)}=1$
The equation represent an ellipse.

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