Question

If the focal distance of the one end of the minor axis of standard ellipse is k and distance between its foci is `2h(kgth)`, then find its equation.

Answer 1

Equation of standard equation is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
Distance between foci=2ae =2h (given)
`rArr ae=h" ".....(1)` ltbr. Also, given, that focal distance of he one end of minor axis is k.
`:. A=k`
`rArr b^(2)=a^(2)-a^(2)e^(2)=k^(2)-H^(2)`
So, the equation of the ellipse is `(x^(2))/(k^(2))+(y^(2))/(k^(2)-h^(2))=1`