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find the eccentricity of the ellipse whose foci are (2,4) and (14,9) and touches the x axis

find the eccentricity of the ellipse whose foci are (2,4) and (14,9) and touches the x axis

Grade:upto college level

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
7 years ago

since ellipse touches the x-axis, therefore x-axis is a tangent to the ellipse. The product of the perpendicular distance is equal to square of the semi minor.

Therefore b2=9*4=36

distance between focii = 2ae=13

ae=13/2

a2-b2=169/4

a2=169/4 + 36 =313/4

e= square root of( a2-b2/a2)=square root of(313/36)


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