Question

# Find the equation of an ellipse, the distance between the foci is 8 units and the distance between the directions is 18 units.

Solution

## Let the equation of the ellipse be x2a2+y2b2=1 ...(i) We have, 2ae=8 [given] ⇒e=82a ⇒e=4a ...(ii) Now, 2ae=18 [given] ⇒a=18e2 ⇒a=9e ...(iii) Using equation (ii) and equation (iii), we get a=9×4a ⇒a2=36 Now, b2=a2(1−e2) ⇒b2=36−(ae)2 ⇒b2=36−16 ⇒b2=20 Putting a2=36 in b2=20 in equation (i), we get x236+y220=1 This is the equation of the required ellipse. MathematicsRD SharmaStandard XI

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