find the equation of an ellipse

Centre is at orgin,major axis is along x axis,e=2/3 and passess throught the point (2,-5/3)

1. let eqn. of the ellipse be x²/a² + y²/b² = 1...........................($)

Now pass the points    as it satifies the ellipse!

You will get a eqn. in the form of a and b

2. Now, as we know that

b²=a²(e²-1).............................(@)

eccentricity is given = 2/3

put in the eqn. (@) u will get an another eqn. in the form of a and b

3. nOw u have two variables and two eqns. solve them and get the values kif a  and b!

4. Put the values of a and b into the eqn. of the ellipse

eqn............($)

and get the eqn of the ellipse!

Hope it helped u!