How do you write an equation of an ellipse in standard form passing through the center at the origin that passes through the points (1, (-10√2)/3 ) and (-2, (5√5)/3 )?
The standard form of the equation of an ellipse is:
We are given that the center is the origin,
Use the two given points and equation  to write two equations:
Convert to an augmented matrix :
Perform Elementary row operations :
Substitute this into equation :
Equation  is the answer.