# Identify the type of conic section whose equation is given. Given: displaystyle{2}{x}^{2}={y}^{2}+{2} To determine: The type of conics.

Identify the type of conic section whose equation is given.
Given:
$2{x}^{2}={y}^{2}+2$
To determine: The type of conics.
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Explanation:
The given equation can be written as,
$2{x}^{2}={y}^{2}+2$
$⇒2{x}^{2}-{y}^{2}=2$
$⇒{x}^{2}-\frac{{y}^{2}}{2}=1$
It is know that the equation of type $\frac{{\left(x-\alpha \right)}^{2}}{{a}^{2}}-\frac{{\left(y-\beta \right)}^{2}}{{b}^{2}}=1$ forms a Hyperbola,
Thus this conic is a Hyperbola.