Ellipse

Q1. Determine the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), the major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Q2. Determine the equation of the ellipse whose foci are (4,0) and (-4,0), eccentricity = ⅓.

(Ans: x² / 9 + y²/8 = 16)

Q3. Find the equation of an ellipse whose eccentricity is 2/3, latus rectum is 5 and the center is (0,0).

Q4. Find the equation of the ellipse whose major axis is on the x-axis and passes through the points (1,4) and (-6,1)

Q5. Find the equation of the ellipse with the center at the origin, the major axis on the x-axis, and passing through the point (4,3) and (-1,4)..

Q6. The foci of an ellipse are (0,±2) and its eccentricity is 1/√2. Find its equation.