Question

If the focal distance of an end of the minor axis of an ellipse is "k" and the distance between foci is 2h, then its equation is.

Answer 1

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focal distance of end of mirror Axis equal to K .

=> a²e² + b² = k²

=> a²e² + a²(1-e²) = k²

=> a² = k²

=> a = k

distance between foci = 2ae = 2h

=> ae = h

So , e = h/a

=> e² = h²/a²

=> e² = h²/k²

Now, b² = a²(1-e²) = k² ( 1- h²/k²)

=> b² = k² - h²

Therefore , equation of ellipse is

=> x²/k² + y²/(k²-h²) = 1
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Answer 2

Answer:

Step-by-step explanation:

focal distance of end of mirror Axis equal to K .

=> a²e² + b² = k²

=> a²e² + a²(1-e²) = k²

=> a² = k²

=> a = k

distance between foci = 2ae = 2h

=> ae = h

So , e = h/a

=> e² = h²/a²

=> e² = h²/k²

Now, b² = a²(1-e²) = k² ( 1- h²/k²)

=> b² = k² - h²

Therefore , equation of ellipse is

=> x²/k² + y²/(k²-h²) = 1