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How to find eccentricity,vertices,directrices of elipse 5x.x+5y.y+6x.y-8=0.Please give steps also.

How to find eccentricity,vertices,directrices of elipse 5x.x+5y.y+6x.y-8=0.Please give steps also.

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear student,

The eccentricity of the ellipse (commonly denoted as either e or ε) is

e=\varepsilon=\sqrt{\frac{a^2-b^2}{a^2}}     =\sqrt{1-\left(\frac{b}{a}\right)^2}

(where again a and b are one-half of the ellipse's major and minor axes respectively) or, as expressed in terms using the flattening factor  f=1-\frac {b}{a}=1-\sqrt{1-e^2},

e=\sqrt{f(2-f)}.

The distance from the center to either focus is ae, or simply \sqrt{a^2-b^2}.

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