find the eccentricity of the conic 2x2-y2=4 - Maths - Conic Sections

Question

find the eccentricity of the conic
2x2-y2=4

Santosh Kumar · Accepted Answer

Equation of the conic : 2x2 â€“ y2 = 4 Dividing both sides by 4, $\frac{2 x^{2}}{4} - \frac{y^{2}}{4} = 1 \Rightarrow \frac{x^{2}}{2} - \frac{y^{2}}{4} = 1 \Rightarrow \frac{x^{2}}{(\sqrt{2})^{2}} - \frac{y^{2}}{(2)^{2}} = 1 (i)$ This is equation of a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (ii)$ Comparing equation (i) and (ii), $a = \sqrt{2} and b = 2$ $∴ Eccentricity, e = \sqrt{1 + \frac{b^{2}}{a^{2}}} \Rightarrow e = \sqrt{1 + \frac{(2)^{2}}{(\sqrt{2})^{2}}} \Rightarrow e = \sqrt{1 + \frac{4}{2}} \Rightarrow e = \sqrt{1 + 2} \Rightarrow e = \sqrt{3}$