if the focal distance of the end of minor axis of an ellipse is q and distance between its foci - Maths - Conic Sections

Question

if the focal distance of the end of minor axis of an ellipse is q
and distance between its foci is 2p,then find its equation

Aarushi Mishra · Accepted Answer

GivenS'S=2pS'M=qWe know distance between focii=2aeS'S=2ae=2pae=p  ________________ 1Sum of distances of a point on ellipse, from focus is constant and is equal to 2aS'M+SM=2aBy syymetryS'M=SM=qq+q=2a2q=2aa=qput in equation 1qe=pe=pqWe knowb2=a21-e2=q21-pq2=q2q2-p2qb2=q2-p2Equation os ellipsE: x2a2+y2b2=1 or x2b2+y2a2=1 depending upon orientationE:x2q2+y2q2-p2=1 or x2q2-p2+y2q2=1

if the focal distance of the end of minor axis of an ellipse is q and distance between its foci is 2p,then find its equation.