SOLUTION: Hello there, I have been stuck on a math problem for hours and have no idea of how to find the solution. Please help me solve the following equation: Find an equation in standard

Ellipse with the center at origin has the standard form equation


     +  = 1.      (1)


The coefficients  "a"  and  "b"  of this equation are the ellipse's semi-axis lengths.

These coefficients are UNKNOWN now, and our task is to find them.

For it, we will use this info about the points (5,6) and (-3,7.06), that they belong to the ellipse.


We substitute coordinates of these points into equation (1): it will give us
two equations, from which we will determine "a"  and  "b".


So, first point gives us THIS equation

     +  = 1.           (2)


Second points gives us THIS equation

      +  = 1.    (3)


From the first glance, these equations are non-linear relative "a" and "b".

But they are LINEAR relative    and  .

So, we consider these two equations as the system of linear equations for    and  .

We solve this system of equations. It can be done by different methods.

It is assumed that the student knows all appropriate methods of linear algebra: substitution, elimination, the determinant method.

I used the determinant methos - same as the Cramer's rule.


So, without submerging into details, I got these solutions:   = 0.015013285  and   = 0.017351885.


It gives me values for  "a"  and  "b" :  a =  = 8.16135248  and  b =  = 7.591483715.


Finally, the standard form equations of the ellipse are


     +  = 1.    (4)


This equation is the ANSWER to the problem's question.

The last step, which should be done, is to check if the answer is correct.

For it, the coordinates of given points should be substituted and left side should be calculated.

I did this check for both points and CONFIRMED the answer.